Black hole

A black hole represents an astronomical entity of such extreme compactness that its gravitational pull precludes the escape of any matter or radiation, including light. Albert Einstein's theory of general relativity, which conceptualizes gravitation as the curvature of spacetime, posits that any mass attaining sufficient compactness will inevitably form a black hole. The demarcation point beyond which escape is impossible is termed the event horizon. Within the framework of general relativity, an object traversing a black hole's event horizon becomes irrevocably confined, yet this transition elicits no locally discernible alteration. Furthermore, general relativity forecasts that each black hole possesses a central singularity, characterized by an infinite curvature of spacetime.

A black hole is an astronomical body so compact that its gravity prevents anything, including light, from escaping. Albert Einstein's theory of general relativity, which describes gravitation as the curvature of spacetime, predicts that any sufficiently compact mass will form a black hole. The boundary of no escape is called the event horizon. In general relativity, crossing a black hole's event horizon traps an object inside but produces no locally detectable change. General relativity also predicts that every black hole should have a central singularity, where the curvature of spacetime is infinite.

The theoretical concept of celestial bodies possessing gravitational fields potent enough to prevent light's escape emerged during the 18th century. By 1916, the initial solution within general relativity capable of characterizing a black hole was discovered. Toward the close of the 1950s, this particular solution started to be physically construed as a spatial region from which no entity could egress. For an extended period, black holes were regarded primarily as a mathematical anomaly; it was only in the 1960s that theoretical investigations demonstrated their status as a generic prediction of general relativity. Cygnus X-1, independently identified by multiple researchers in 1971, became the first black hole to achieve widespread scientific acceptance.

Black holes characteristically originate from the gravitational collapse of exceptionally massive stars at the culmination of their stellar life cycles. Subsequent to its formation, a black hole can augment its mass through the accretion of matter from its ambient environment. Supermassive black holes, possessing masses equivalent to millions of solar masses, can emerge either through the absorption of stars and coalescence with other black holes, or by the direct collapse of vast gas clouds. A prevailing scientific consensus affirms the presence of supermassive black holes within the central regions of the majority of galaxies.

Quantum field theory, when applied to curved spacetime, postulates that event horizons emit Hawking radiation, with the emission rate exhibiting an inverse proportionality to the black hole's mass. Consequently, this phenomenon induces a gradual mass loss in the black hole, contingent upon the absence of matter accretion. Nevertheless, even the smallest observed category of black holes, known as stellar black holes, accumulate mass from the cosmic microwave background at a rate exceeding their mass loss through Hawking radiation.

The existence of a black hole can be deduced indirectly by observing its interactions with surrounding matter and electromagnetic radiation, including visible light. Matter spiraling towards a black hole may coalesce into an accretion disk composed of infalling plasma, which becomes heated by frictional forces and subsequently emits radiation. Under extreme conditions, this process generates a quasar, recognized as among the most luminous celestial objects in the cosmos. The coalescence of black holes is detectable through the gravitational waves they propagate. When stars orbit a black hole, their orbital dynamics provide a means to ascertain the black hole's mass and spatial coordinates. Through these methodologies, astronomers have identified numerous candidate stellar black holes within binary systems and have conclusively determined that Sagittarius A*, the radio source situated at the galactic core of the Milky Way, harbors a supermassive black hole estimated at approximately 4.3million solar masses.

Historical Context

The conceptualization of a celestial body so massive that even light could not escape its gravitational pull was initially advanced in the late 18th century by the English astronomer and clergyman John Michell, and independently by the French scientist Pierre-Simon Laplace. In contrast to the contemporary understanding of an exceedingly dense object, both scholars posited the existence of exceptionally large stars.

In a concise section of a letter published in 1784, Michell's hypothesis posited that a star possessing the same density but 500 times the solar radius would prevent the escape of any emitted light, as its surface escape velocity would surpass the speed of light. Michell accurately theorized that such non-radiating celestial entities could be discerned via their gravitational influence on proximate visible bodies. In 1796, within his treatise Exposition du Système du Monde, Laplace, while contemplating the genesis of the Solar System, qualitatively proposed that a star might become imperceptible if it attained a sufficient magnitude. Franz Xaver von Zach subsequently requested a mathematical analysis from Laplace, which Laplace furnished and published in von Zach's periodical, Allgemeine Geographische Ephemeriden.

General Relativity Theory

In 1905, Albert Einstein demonstrated the invariance of the laws of electromagnetism for observers moving at differing relative velocities. The principles of mechanics had previously been established as invariant under similar conditions. Nevertheless, the theory of gravitation remained to be integrated into this framework.

In 1907, Einstein published a paper proposing his equivalence principle, which posited that inertial mass and gravitational mass share a common origin. Leveraging this principle, Einstein forecasted both the gravitational redshift and the lensing effect of gravity on light. His initial prediction for gravitational lensing, however, represented only half the value later derived from the complete theory of general relativity. By 1915, Einstein had further developed these concepts into his general theory of relativity, elucidating how matter influences spacetime, which subsequently dictates the movement of other matter. This foundational work laid the groundwork for the field of black hole physics.

Singular Solutions in General Relativity

Merely months following Einstein's publication of the field equations for general relativity, astrophysicist Karl Schwarzschild endeavored to apply this theoretical framework to stars. Assuming spherical symmetry and an absence of spin, he successfully derived a solution to Einstein's equations. Independently, a few months after Schwarzschild, Johannes Droste, a student of Hendrik Lorentz, presented an identical solution. The Schwarzschild solution exhibited a singularity at a specific radius from the mass's center, indicating that certain terms within Einstein's equations diverged to infinity. The fundamental characteristics of this radius, subsequently designated as the Schwarzschild radius, remained uncomprehended during that period.

Numerous physicists in the early 20th century expressed skepticism regarding the actual existence of black holes. In a 1926 popular science publication, Arthur Eddington criticized the concept of a star compressed to its Schwarzschild radius, interpreting it as a deficiency within the then-imperfectly understood theory of general relativity. By 1939, Einstein himself employed his general theory of relativity in an effort to demonstrate the impossibility of black holes. His argument posited that either escalating pressure or increasing centrifugal force would counteract gravitational attraction, thereby preventing an object from collapsing beyond its Schwarzschild radius. However, he overlooked the potential for implosion to propel the system past this critical threshold.

Gravity Versus Degeneracy Pressure

By the 1920s, astronomers had categorized several white dwarf stars whose low temperatures and high densities defied explanation through the conventional cooling processes of ordinary stars. In 1926, Ralph Fowler demonstrated that these stars differ fundamentally from main-sequence stars, where thermal pressure counteracts gravity. Instead, a distinct form of quantum-mechanical pressure provides the gravitational counterbalance at these extreme temperatures and densities. In 1931, Subrahmanyan Chandrasekhar investigated the novel state of matter arising from this equilibrium, termed electron-degenerate matter, and ascertained its stability below a specific limiting mass. By 1934, he further showed that this discovery accounted for the observed population of white dwarf stars. Upon Chandrasekhar's announcement of his findings, Eddington contended that stars exceeding this limit would continue to radiate until their density became sufficient to impede light escape, a conclusion he deemed preposterous. Eddington, and subsequently Lev Landau, posited that an as-yet-undiscovered mechanism would ultimately halt such a collapse.

During the 1930s, Fritz Zwicky and Walter Baade conducted research on stellar novae, specifically concentrating on exceptionally luminous events they designated as supernovae. Zwicky advanced the hypothesis that supernovae generated stars possessing the density of atomic nuclei, known as neutron stars; however, this concept received minimal attention at the time. In 1939, building upon Chandrasekhar's theoretical framework, J. Robert Oppenheimer and George Volkoff predicted that neutron stars below a specific mass threshold, later identified as the Tolman–Oppenheimer–Volkoff limit, would maintain stability due to neutron degeneracy pressure. Beyond this limit, they theorized that either their model would become inapplicable or that gravitational contraction would proceed indefinitely.

John Archibald Wheeler, along with two of his students, addressed outstanding questions concerning the theoretical model underpinning the Tolman–Oppenheimer–Volkoff (TOV) limit. In 1965, Harrison and Wheeler formulated the equations of state that correlate density with pressure for cold matter, encompassing both electron degeneracy and neutron degeneracy regimes. Subsequently, Masami Wakano and Wheeler employed these equations to calculate the equilibrium curve for stars, establishing a relationship between stellar mass and circumference. Their investigations revealed no supplementary characteristics that would undermine the validity of the TOV limit. Consequently, the sole mechanism capable of precluding black hole formation was identified as a dynamic process involving the expulsion of adequate mass from a cooling star.

Genesis of the Modern Model

The contemporary understanding of black holes was established in 1939 by Robert Oppenheimer and his student Hartland Snyder. Their seminal paper presented a solution to Einstein's equations of general relativity for an idealized imploding star, a theoretical construct subsequently termed the Oppenheimer–Snyder model. This work detailed the observable phenomena from a distant perspective. Initially, the stellar material undergoes a rapid inward collapse. Nevertheless, as the star's density intensifies, gravitational time dilation progressively increases, causing the collapse, when observed from afar, to appear to decelerate until the star attains its Schwarzschild radius, at which point it seems to become static in time.

In 1958, David Finkelstein characterized the Schwarzschild surface as an event horizon, describing it as "a perfect unidirectional membrane: causal influences can cross it in only one direction". This implies that occurrences within a black hole are causally disconnected from events outside it. Finkelstein subsequently developed a novel reference frame that incorporated the perspective of infalling observers. This new framework facilitated the correlation of events at the surface of an imploding star with those observed from a significant distance. By 1962, the convergence of these two viewpoints largely persuaded skeptics regarding the physical plausibility of stellar implosion into a black hole.

The Golden Age of Black Hole Research

The period spanning from the mid-1960s to the mid-1970s is recognized as the "golden age of black hole research," a transformative era during which general relativity and the study of black holes transitioned into prominent areas of scientific inquiry.

During this epoch, significant advancements included the discovery of solutions to the equations of general relativity under diverse physical constraints. Notably, in 1963, Roy Kerr derived the precise solution for a rotating black hole. Subsequently, in 1965, Ezra Newman identified the cylindrically symmetric solution for a black hole possessing both rotation and an electric charge.

In 1967, Werner Israel demonstrated that the Schwarzschild solution represented the sole possible configuration for a non-rotating, uncharged black hole, implying that such a black hole is uniquely characterized by its mass. Analogous identities were subsequently established for Reissner-Nordström and Kerr black holes, which are defined exclusively by their mass and either their charge or spin, respectively. Collectively, these discoveries culminated in the formulation of the no-hair theorem, which posits that a stationary black hole is entirely delineated by the three parameters of the Kerr–Newman metric: mass, angular momentum, and electric charge.

Initially, there was a prevailing suspicion that the anomalous mathematical singularities inherent in various black hole solutions arose solely from the assumption of perfect spherical symmetry, suggesting that such singularities might not manifest in more general, asymmetric black hole scenarios. This perspective was notably championed by Vladimir Belinski, Isaak Khalatnikov, and Evgeny Lifshitz, who endeavored to demonstrate the absence of singularities in generic solutions, though they later recanted their stance. Nevertheless, in 1965, Roger Penrose conclusively proved that general relativity mandates the presence of singularities in all black holes, a conclusion that may require re-evaluation when quantum mechanical effects are considered.

Concurrently, astronomical observations experienced substantial progress during this period. In 1967, Antony Hewish and Jocelyn Bell Burnell discovered pulsars, which by 1969 were identified as rapidly rotating neutron stars. Prior to this, neutron stars, much like black holes, were largely considered theoretical constructs. However, the discovery of pulsars underscored their physical significance, stimulating increased interest in various compact objects potentially formed through gravitational collapse. Building upon observations conducted in Greenwich and Toronto in the early 1970s, Cygnus X-1, a galactic X-ray source initially identified in 1964, gained widespread acceptance as the first astronomical object confirmed to be a black hole.

The foundational principles of black hole thermodynamics were established in the early 1970s through the collaborative efforts of James Bardeen, Jacob Bekenstein, Carter, and Hawking. These principles elucidate black hole behavior by drawing parallels with the established laws of thermodynamics. Within this framework, a black hole's mass, surface area, and surface gravity correspond respectively to the thermodynamic quantities of energy, entropy, and temperature. The analogy reached its culmination in 1974 when Hawking demonstrated, using quantum field theory, that black holes are predicted to emit radiation akin to a black body, with a temperature directly proportional to their surface gravity, a phenomenon now recognized as Hawking radiation.

Contemporary Research and Observational Findings

By late 1973, the stellar-mass black hole Cygnus X-1 had achieved widespread scientific acceptance; however, several decades elapsed before supermassive black holes garnered comparable recognition. Despite early proposals in the 1960s by physicists like Donald Lynden-Bell and Martin Rees, who posited that accreting supermassive black holes fueled the energetic quasars at galactic centers, empirical evidence remained scarce. The launch of the Hubble Space Telescope in the 1990s provided crucial data, revealing that supermassive black holes were not merely confined to active galactic nuclei but were, in fact, ubiquitous at the core of nearly every galaxy. Black holes situated in quiescent galaxies exhibit slower accretion rates or less efficient radiation processes.

In 1999, David Merritt introduced the M–sigma relation, a correlation linking the velocity dispersion of matter within a galaxy's central bulge to the mass of the supermassive black hole residing at its core. This correlation was subsequently validated by further research. Concurrently, independent research teams, spearheaded by Andrea Ghez and Reinhard Genzel, utilized telescopic observations of stellar velocities in the Milky Way's galactic center to deduce that Sagittarius A*, a compact radio source, was highly probable to be a supermassive black hole.

The LIGO Scientific Collaboration and Virgo Collaboration achieved the inaugural direct detection of gravitational waves, designated GW150914, in late 2015, marking the first observed black hole merger event. During this merger, the black holes were situated approximately 1.4 billion light-years from Earth and possessed masses roughly 30 and 35 times that of the Sun. In recognition of their leadership in this project, Rainer Weiss, Kip Thorne, and Barry Barish were jointly awarded the Nobel Prize in Physics in 2017. Since this initial breakthrough in 2015, hundreds of additional gravitational wave events have been recorded.

On April 10, 2019, the Event Horizon Telescope (EHT) published the first direct image of a black hole and its immediate surroundings, based on observations conducted in 2017 of the supermassive black hole located in Messier 87's galactic center. Subsequently, in 2022, the Event Horizon Telescope collaboration released an image of Sagittarius A*, the black hole at the center of the Milky Way galaxy, utilizing data acquired in 2017.

The Nobel Prize in Physics in 2020 recognized significant contributions to the understanding of black holes. Andrea Ghez and Reinhard Genzel were jointly awarded half of the prize for their discovery confirming Sagittarius A* as a supermassive black hole. Roger Penrose received the other half for his theoretical work demonstrating that the mathematical framework of general relativity necessitates the formation of black holes. The scientific community expressed regret that Stephen Hawking's profound theoretical contributions to black hole physics could not be honored, as he had passed away in 2018.

Etymology

In December 1967, a student reportedly proposed the phrase black hole during a lecture by John Wheeler, who subsequently adopted the term due to its conciseness and "advertising value." Wheeler's prominence in the field ensured its rapid acceptance, leading some to attribute the coinage of the phrase to him. Nevertheless, the term was concurrently employed by others. Science writer Marcia Bartusiak attributes the term black hole to physicist Robert H. Dicke, who, in the early 1960s, allegedly likened the phenomenon to the Black Hole of Calcutta, infamous as a prison where individuals entered but never departed alive. The term appeared in print in Life and Science News magazines in 1963, and in science journalist Ann Ewing's article "'Black Holes' in Space," published on January 18, 1964, which reported on a meeting of the American Association for the Advancement of Science held in Cleveland, Ohio.

Definition

A black hole is conventionally defined as a region of spacetime from which no information-carrying signals or objects can escape. However, verifying an object as a black hole by this definition would necessitate an infinite observation period and an infinite distance from the black hole to confirm that nothing has indeed escaped, rendering it impractical for identifying a physical black hole. Several alternative definitions exist to describe or identify a black hole, though they lack universal consensus among physicists. Among astrophysicists, a black hole is characterized as a compact object possessing a mass exceeding four solar masses. A black hole may also be conceptualized as an information reservoir or a region where space collapses inward faster than the speed of light.

Properties

The no-hair theorem posits that, upon achieving a stable state post-formation, a black hole is characterized by only three independent physical properties: mass, electric charge, and angular momentum; the black hole is otherwise devoid of distinguishing features. If this conjecture holds true, any two black holes sharing identical values for these parameters would be indistinguishable. The extent to which this conjecture is accurate remains an unresolved problem.

The simplest static black holes, designated Schwarzschild black holes, possess mass but lack both electric charge and angular momentum. Non-rotating charged black holes are described by the Reissner–Nordström metric, whereas the Kerr metric characterizes a non-charged rotating black hole. The most comprehensive stationary black hole solution currently known is the Kerr–Newman metric, which describes a black hole exhibiting both charge and angular momentum.

Mass

The most basic static black holes possess mass but are devoid of electric charge or angular momentum. Contrary to the common misconception of a black hole "sucking in everything" within its vicinity, its external gravitational field, when observed from a distance, is identical to that of any other body of equivalent mass.

A black hole's mass can theoretically be any positive value, but its electric charge and angular momentum are constrained by its mass, with more massive black holes permitting higher limits. Specifically, the net electric charge ${\displaystyle Q}$ and the total angular momentum ${\displaystyle J}$ must satisfy the following inequality for a black hole of mass ${\displaystyle M}$: Q §4445§ §4950§ π<!-- π --> ϵ<!-- ϵ --> §5960§ + c §7576§ J §8384§ G M §9596§ ≤ G M §111112§ {\displaystyle {\frac {Q^{2}}{4\pi \epsilon _{0}}}+{\frac {c^{2}J^{2}}{GM^{2}}}\leq GM^{2}} , where ϵ<!-- ϵ --> §150151§ {\displaystyle \epsilon _{0}} denotes the vacuum permittivity constant, ${\displaystyle c}$ represents the speed of light, and ${\displaystyle G}$ is the gravitational constant. Black holes that achieve the maximal permissible combination of charge and spin, as defined by this inequality, are termed extremal black holes. While solutions to Einstein's equations that violate this inequality exist, these theoretical objects lack an event horizon and are known as naked singularities, which would be observable externally. Given that such singularities would render the universe fundamentally unpredictable, many physicists contend that their existence is impossible. The weak cosmic censorship hypothesis, proposed by Penrose, posits that such singularities cannot form through the gravitational collapse of realistic matter. However, this hypothesis remains unproven, and some physicists maintain that naked singularities might exist. Furthermore, it is uncertain whether black holes can actually reach an extremal state and form naked singularities, as natural physical processes tend to counteract increases in spin and charge when a black hole approaches extremality.

The total mass of a black hole can be ascertained by analyzing the orbital dynamics of proximate celestial bodies, including stars or gas clouds.

Spin and Angular Momentum

All black holes exhibit rotation, frequently at high velocities; for instance, the supermassive black hole GRS 1915+105 is estimated to rotate at more than 1,000 revolutions per second. Similarly, Sagittarius A*, the supermassive black hole at the center of the Milky Way, rotates at approximately 90% of its theoretical maximum rate.

The spin rate of a black hole can be deduced through analyses of atomic spectral lines within the X-ray range. As gas accretes near the black hole, high-energy X-ray emission from electron-positron pairs irradiates more distant gas, exhibiting relativistic redshift. The specific radial distance at which this accretion occurs, along with the distinct redshift magnitudes, varies depending on the black hole's spin. Astronomers utilize the spectral separation between the X-ray emission from the outer accretion disk and the redshifted emission originating from the infalling matter to ascertain the black hole's spin.

An alternative approach for spin estimation relies on the thermal properties of gas accreting onto the black hole. This technique necessitates independent determinations of the black hole's mass and the accretion disk's inclination angle, subsequently employing computational modeling. Furthermore, gravitational waves generated by coalescing binary black holes offer insights into the spins of both the progenitor black holes and the resulting merged entity; however, such phenomena are infrequent.

The presence of spin endows a black hole with angular momentum. Observations indicate that the supermassive black hole situated at the core of the Messier 87 (M87) galaxy possesses an angular momentum approaching its theoretical maximum. By setting the charge ${\displaystyle Q}$ to zero, the maximum spin of an uncharged black hole can be expressed as $${\displaystyle J\leq {\frac {GM^{2}}{c}},}$$ which facilitates the definition of a dimensionless spin magnitude, constrained by §6162§ ≤ c J G M §8182§ ≤ 1. {\displaystyle 0\leq {\frac {cJ}{GM^{2}}}\leq 1.}

Charge

The majority of black holes are hypothesized to possess an approximately neutral electric charge. For instance, research by Michal Zajaček, Arman Tursunov, Andreas Eckart, and Silke Britzen determined that the electric charge of Sagittarius A* is at least ten orders of magnitude lower than its theoretical maximum. A black hole carrying an electric charge would repel other charges of the same polarity, consistent with the behavior of any charged entity. Should a black hole acquire a net charge, particles with opposing charges would be attracted by the additional electromagnetic force, whereas similarly charged particles would be repelled, thereby facilitating the black hole's neutralization. This neutralizing mechanism might be attenuated if the black hole simultaneously possesses spin. The existence of an electric charge can diminish the black hole's event horizon diameter by as much as 38%.

For a non-spinning black hole, the electric charge $${\displaystyle Q\leq {\sqrt {G}}M,}$$ is constrained, where G represents the gravitational constant and M denotes the black hole's mass.

Classification

Black holes are categorized based on their formation mechanisms and their masses (typically expressed in solar masses, M_☉); however, these classification criteria are intrinsically linked. Stellar-mass black holes originate from the gravitational collapse of massive stars. The lower mass limit for black holes resulting from stellar gravitational collapse is determined by the maximum stable mass of a neutron star, estimated to be between 2 and 4 M_☉. Conversely, hypothetical primordial black holes, theorized to have emerged shortly after the Big Bang, could possess significantly smaller masses, potentially as low as 10⁻⁵ grams at their inception. Such exceedingly small black holes are occasionally referred to as micro black holes.

Stellar black holes exhibit a broad spectrum of masses. While estimates for their maximum initial mass vary, they typically fall within the range of 10 to 100 M_☉, with larger masses projected for black holes originating from low-metallicity stars. These black holes can accumulate additional mass through the accretion of surrounding material, frequently sourced from a companion object like a star, or through mergers with other black holes.

Intermediate-mass black holes (IMBHs) represent a category of black holes larger than stellar black holes but smaller than supermassive black holes, possessing masses approximately between 10§34§ and 10§910§ M_☉. These entities appear less common than their stellar and supermassive counterparts, with only a limited number of candidates currently identified. Theoretical propositions suggest that IMBHs might originate from collisions within globular and star clusters, or at the core of low-mass galaxies. Furthermore, their formation could result from the coalescence of smaller black holes, as evidenced by several LIGO observations detecting merged black holes with masses ranging from 110 to 350 M_☉.

Supermassive black holes (SMBHs) represent the most massive category, exceeding 10⁶ M_☉ in mass. These colossal objects are hypothesized to reside at the cores of nearly all large galaxies, including the Milky Way. A distinct subcategory of even larger black holes, termed ultramassive black holes, has been posited by some researchers, characterized by masses surpassing §121314§-§181920§ M_☉. Theoretical frameworks suggest that the accretion disk supplying material to black holes becomes unstable once a black hole attains a mass between 50ק303132§ and 100ק383940§ M_☉, thereby establishing an approximate upper bound for black hole mass.

Structure

Although black holes are theoretically perceived as invisible gravitational sinks for all matter and light, their immense gravitational influence in astrophysical environments modifies the trajectories of proximate celestial bodies and draws in adjacent gas at relativistic velocities, rendering the regions surrounding black holes among the most luminous phenomena in the cosmos.

External Geometry

Relativistic Jets

Certain black holes exhibit relativistic jets, which are attenuated streams of plasma propelled away from the black hole at speeds exceeding one-tenth the speed of light. A minor portion of the infalling matter is accelerated outward along the black hole's rotational axis. These powerful jets can traverse distances spanning millions of light-years from their origin.

Relativistic jets can emanate from black holes across the entire mass spectrum. Nevertheless, they are predominantly detected in association with rotating black holes possessing highly magnetized accretion disks. Such jets were more prevalent in the early universe, a period characterized by the rapid mass accumulation of galaxies and their central supermassive black holes. While all jet-producing black holes are accompanied by an accretion disk, the jets themselves generally surpass the disk in luminosity. Quasars, commonly located in external galaxies, are hypothesized to be supermassive black holes generating jets, whereas microquasars are thought to be stellar-mass objects with jets, frequently observed within the Milky Way.

The precise mechanism underlying jet formation remains undetermined, though multiple hypotheses have been advanced. One proposed method for powering these jets is the Blandford-Znajek process, which posits that the rotational dragging of magnetic field lines by a black hole could propel matter jets into the cosmos. The Penrose process, involving the extraction of a black hole's rotational energy, has also been suggested as a plausible mechanism for jet propulsion.

Accretion Disk

In accordance with the principle of angular momentum conservation, gas accreting into the gravitational potential well of a massive object typically coalesces into a disk-shaped structure encircling that object. As the disk's angular momentum is redistributed outwards through internal dynamics, its constituent matter spirals further inward, transforming gravitational potential energy into thermal energy and emitting substantial quantities of X-rays. The temperatures within these disks can span from thousands to millions of kelvins, with considerable variations observed across a single accretion disk. Furthermore, accretion disks are capable of emitting radiation across other segments of the electromagnetic spectrum, influenced by factors such as the disk's turbulence, magnetization, and the black hole's mass and angular momentum.

Accretion disks are categorized as either geometrically thin or geometrically thick. Geometrically thin disks are primarily restricted to the black hole's equatorial plane and exhibit a distinct boundary at the innermost stable circular orbit (ISCO), whereas geometrically thick disks derive support from internal pressure and temperature, enabling them to extend within the ISCO. Disks characterized by high rates of electron scattering and absorption, which appear luminous and opaque, are designated as optically thick; conversely, optically thin disks exhibit greater translucency and yield less intense images when observed remotely. Accretion disks associated with black holes accreting beyond the Eddington limit are frequently termed polish donuts owing to their substantial, toroidal morphology, which resembles a donut.

Quasar accretion disks are generally anticipated to exhibit a blue coloration. In contrast, the disk associated with a stellar black hole is projected to manifest as orange, yellow, or red, with its innermost regions displaying the highest luminosity. Theoretical investigations indicate that a disk's temperature correlates with its bluer appearance; however, this correlation is not consistently corroborated by empirical observations of celestial bodies. Furthermore, accretion disk colors can also undergo modification due to the Doppler effect, where the segment of the disk approaching an observer appears bluer and more luminous, while the segment receding from the observer manifests as redder and less luminous.

Innermost stable circular orbit (ISCO)

Under Newtonian gravitational theory, test particles are capable of maintaining stable orbits at any distance from a central mass. Conversely, in general relativity, a minimum radius exists below which a massive particle cannot sustain a stable orbit. Minor inward perturbations to this specific orbit will inevitably cause the particle to spiral into the black hole, whereas outward perturbations may result in the particle spiraling inward, transitioning to a more distant stable orbit, or escaping to infinity, contingent upon its energy. This particular orbit is designated as the innermost stable circular orbit (ISCO). The precise location of the ISCO is influenced by both the black hole's spin and the intrinsic spin of the orbiting particle. For a Schwarzschild black hole (characterized by zero spin) and a non-spinning particle, the ISCO's position is defined by: r I S C O = §2627§ r s = §4344§ G M c §5657§ , {\displaystyle r_{\rm {ISCO}}=3\,r_{\text{s}}={\frac {6\,GM}{c^{2}}},} where ${\displaystyle r_{\rm {_{ISCO}}}}$ represents the radius of the ISCO, ${\displaystyle r_{\text{s}}}$ denotes the Schwarzschild radius of the black hole, ${\displaystyle G}$ signifies the gravitational constant, and ${\displaystyle c}$ refers to the speed of light. The radius of this orbit exhibits minor variations contingent upon the particle's spin. In the presence of charged black holes, the ISCO shifts to a smaller radius. For rotating black holes, the ISCO is displaced inward for particles orbiting in the same direction as the black hole's rotation (prograde motion) and outward for particles orbiting in the opposing direction (retrograde motion). For instance, a particle in a retrograde orbit may have an ISCO located as far as approximately ${\displaystyle 9r_{\text{s}}}$, whereas a prograde orbiting particle's ISCO can be situated as near as the event horizon itself.

The Photon Sphere and Shadow

The photon sphere represents a spherical boundary where photons, traveling tangentially to its surface, are completely deflected around the black hole, potentially completing multiple orbits. Light rays possessing impact parameters smaller than the photon sphere's radius will inevitably enter the black hole. In the context of Schwarzschild black holes, the photon sphere's radius is 1.5 times the Schwarzschild radius; for non-Schwarzschild black holes, this radius is at least 1.5 times that of the event horizon. From a significant observational distance, the photon sphere manifests an observable black hole shadow. As no light can escape from within the black hole, this shadow delineates the boundary of observable phenomena. The shadow produced by colliding black holes is predicted to exhibit distinctive warped morphologies, thereby enabling researchers to identify black holes on the verge of merging.

Although light can still egress from the photon sphere, any light traversing this boundary on an inward trajectory will inevitably be absorbed by the black hole. Consequently, any light observed externally originating from the photon sphere must have been emitted by entities situated between the photon sphere and the event horizon. Furthermore, light directed towards the photon sphere can also undergo gravitational lensing, curving around the black hole and returning to its point of emission.

The radius of the photon sphere for a rotating, uncharged black hole is contingent upon its spin parameter and the orbital direction of the photon (prograde or retrograde). Prograde-orbiting photons exhibit a photon sphere located between 1 and 3 Schwarzschild radii from the black hole's center, whereas retrograde-orbiting photons have a photon sphere situated between 3 and 5 Schwarzschild radii. The precise positions of these photon spheres are determined by the black hole's rotational magnitude. In the case of a charged, nonrotating black hole, only a single photon sphere exists, and its radius diminishes with an increase in the black hole's charge. For non-extremal, charged, rotating black holes, two distinct photon spheres are consistently present, with their exact radii being dependent on the specific parameters of the black hole.

Ergosphere

In the vicinity of a rotating black hole, spacetime itself undergoes a rotational distortion, akin to a vortex. This rotating spacetime exerts a dragging force, compelling both matter and light to co-rotate with the spinning black hole. This phenomenon, a consequence of general relativity, is termed frame dragging, and its intensity escalates with proximity to the rotating mass. The specific region of spacetime where it becomes impossible for any object to remain stationary is designated as the ergosphere.

The ergosphere of a black hole constitutes a volume delimited by the black hole's event horizon and the ergosurface. This ergosurface converges with the event horizon at the black hole's poles but extends outward from it in the equatorial plane.

Within the ergosphere, both matter and radiation retain the capacity to escape. The Penrose process enables objects to exit the ergosphere possessing greater energy than their initial entry state. This additional energy is derived from the black hole's rotational energy, thereby decelerating the black hole's spin. A specialized variant of the Penrose process, known as the Blandford–Znajek process, which operates in the presence of intense magnetic fields, is hypothesized to be a primary mechanism responsible for the immense luminosity and relativistic jets observed in quasars and other active galactic nuclei.

Plunging Region

The plunging region denotes the observable spacetime area immediately adjacent to a black hole's event horizon. Within this zone, free-falling matter can no longer sustain stable circular orbits or arrest its ultimate descent into the black hole. Instead, it undergoes a rapid plunge towards the black hole, approaching the speed of light, simultaneously experiencing extreme heating and generating a distinctive, detectable thermal emission. Nevertheless, light and radiation originating from this region are still capable of escaping the black hole's gravitational influence.

Radius

For an uncharged, non-rotating black hole, the event horizon's radius, known as the Schwarzschild radius, exhibits direct proportionality to its mass, M, as defined by the following equation: r s = §2324§ G M c §3435§ ≈ 2.95 M M ⊙   k m , {\displaystyle r_{\mathrm {s} }={\frac {2GM}{c^{2}}}\approx 2.95\,{\frac {M}{M_{\odot }}}~\mathrm {km,} } In this formula, r_s denotes the Schwarzschild radius, G represents the gravitational constant, c signifies the speed of light, and M_☉ refers to the Sun's mass. For a black hole possessing the same mass but exhibiting non-zero spin or electric charge, the radius is reduced. As a black hole's charge and spin approach their theoretical maximum limits, the event horizon's radius approaches: r + = G M c §122123§ , {\displaystyle r_{\mathrm {+} }={\frac {GM}{c^{2}}},} This value represents half the radius of an equivalent non-spinning, uncharged black hole.

Given that the volume enclosed by the Schwarzschild radius expands proportionally to the cube of the radius, the average density of a black hole within its Schwarzschild radius is inversely proportional to the square of its mass. Consequently, supermassive black holes exhibit significantly lower densities compared to stellar black holes. For instance, a black hole with a mass of 10⁸ M_☉ possesses an average density comparable to that of water.

The Event Horizon

The fundamental characteristic of a black hole is its event horizon, a spacetime boundary that permits the passage of matter and light exclusively inward, towards the black hole's central singularity. No entity, including light, can egress from within the event horizon. This boundary is termed an "event horizon" because any event transpiring within its confines cannot transmit information or exert influence upon an external observer, thereby precluding any determination of its occurrence. For non-rotating black holes, the event horizon exhibits a perfectly spherical geometry, whereas for rotating black holes, it assumes an oblate shape.

From the vantage point of a distant observer, a clock positioned in proximity to a black hole would register time at a slower rate compared to a clock situated farther away. This phenomenon, termed gravitational time dilation, would also cause an object descending into a black hole to appear to decelerate as it approaches the event horizon, never definitively reaching it from an external observer's perspective. All internal processes within this object would seem to slow, and any emitted light would exhibit increased redness and diminished brightness, an effect known as gravitational redshift. An object commencing its fall from a distance equivalent to half a Schwarzschild radius above the event horizon would progressively dim until it became imperceptible, vanishing from sight within approximately one hundredth of a second. Furthermore, it would appear to flatten onto the black hole's surface, merging with all previously accreted material.

Conversely, an observer traversing the event horizon of a black hole would perceive none of these aforementioned effects. From their subjective viewpoint, their personal chronometers would function normally, and they would cross the event horizon within a finite proper time, without detecting any anomalous behavior. According to the principles of general relativity, the precise location of the event horizon cannot be ascertained through local observations, a consequence of Einstein's equivalence principle.

Internal Geometry

Cauchy Horizon

Rotating and/or charged black holes possess an inner horizon, frequently referred to as the Cauchy horizon, situated within the black hole's interior. This inner horizon is delineated into two distinct segments: an ingoing section and an outgoing section.

Within the ingoing section of the Cauchy horizon, infalling radiation and matter are hypothesized to accumulate, leading to an infinite increase in spacetime curvature at the horizon. Consequently, an observer traversing this region would be subjected to intense tidal forces. This phenomenon is commonly termed mass inflation, as it correlates with an exponential increase in a parameter governing the black hole's internal mass. The resultant accumulation of tidal forces is designated as the mass-inflation singularity or Cauchy horizon singularity. However, certain physicists contend that in astrophysical black holes, the processes of accretion and Hawking radiation would preclude the occurrence of mass inflation.

Conversely, at the outgoing section of the inner horizon, infalling radiation is predicted to backscatter from the black hole's spacetime curvature, subsequently propagating outwards and accumulating at the outgoing Cauchy horizon. This process would induce a gravitational shock wave and significant tidal forces upon an infalling observer, as the spacetime curvature at the horizon diverges to infinity. This specific accumulation of tidal forces is referred to as the shock singularity.

Both of these aforementioned singularities are classified as weak, implying that an object traversing them would experience only a finite deformation due to tidal forces, notwithstanding the infinite spacetime curvature at the singularity itself. This contrasts with a strong singularity, where an object encountering it would undergo infinite stretching and compression. Furthermore, these are characterized as null singularities, indicating that a photon could propagate parallel to them indefinitely without interception.

Singularity

Disregarding quantum effects, every black hole is theorized to contain an internal singularity, defined as a region where spacetime curvature becomes infinite and geodesics terminate within a finite proper time. In the case of a non-rotating black hole, this region manifests as a singular point; however, for a rotating black hole, it extends into a ring singularity situated within the plane of rotation. In both scenarios, the singular region occupies zero volume. The entirety of the black hole's mass is concentrated within this singularity. Consequently, possessing non-zero mass within an infinitesimally small volume, the singularity is conceptualized as having infinite density.

Observers entering a Schwarzschild black hole—characterized as non-rotating and uncharged—are inexorably drawn towards the singularity upon crossing the event horizon. As their descent into the black hole progresses, they would be subjected to escalating tidal forces, a phenomenon colloquially termed spaghettification or the noodle effect. Ultimately, they would reach the singularity and be compressed into an infinitely small point. Nevertheless, the presence of any perturbations, such as those induced by infalling matter or radiation, would cause the spacetime near the singularity to oscillate chaotically. Consequently, any infalling matter would experience intense tidal forces that rapidly shift in direction, concurrently undergoing compression into an progressively diminishing volume.

Alternative formulations of general relativity, particularly those incorporating certain quantum effects, propose the existence of regular or nonsingular black holes, which inherently lack singularities. For instance, the fuzzball model, derived from string theory, posits that black holes are fundamentally composed of quantum microstates and therefore do not necessarily possess a singularity or an event horizon. Similarly, the theory of loop quantum gravity suggests that while the curvature and density at the core of a black hole are substantial, they remain finite rather than infinite.

Formation

Black holes originate from the gravitational collapse of massive stars, occurring either through direct collapse or as a consequence of a supernova explosion in a process termed fallback. Additionally, black holes may form through the merger of two neutron stars or a neutron star with a black hole. More speculative formation pathways encompass primordial black holes, which are theorized to result from density fluctuations in the early universe, the gravitational collapse of hypothetical dark stars—objects powered by the annihilation of dark matter—or from hypothetical self-interacting dark matter.

Supernovae as a Formation Mechanism

Gravitational collapse is initiated when an object's internal pressure is incapable of counteracting its own gravitational force. Towards the culmination of a star's stellar evolution, its hydrogen fuel for fusion becomes depleted, leading to the sequential fusion of progressively heavier elements until an iron core is formed. As the fusion of elements beyond iron is an endothermic process, requiring more energy input than output, nuclear fusion within the core terminates. Should the star's iron core exceed a critical mass, it becomes gravitationally unstable and can no longer sustain itself against its own gravity, precipitating gravitational collapse.

The mass of a black hole formed via a supernova is subject to a lower mass limit; an insufficiently massive progenitor star can be halted from complete collapse by the degeneracy pressure of its constituents, leading to the formation of an exotic, denser state of matter. This degeneracy pressure arises from the Pauli exclusion principle, which dictates that no two identical fermions can occupy the same quantum state simultaneously, thereby creating a resistance to further compression. Progenitor stars with initial masses below approximately 8 M_☉ typically evolve into white dwarfs, where electron degeneracy pressure effectively counteracts gravitational forces. In the case of more massive progenitor stars, gravitational forces overwhelm electron degeneracy pressure, causing further compression until neutron degeneracy pressure provides the necessary resistance, resulting in the formation of a neutron star. However, if the stellar mass is sufficiently greater, even neutron degeneracy pressure proves inadequate to withstand the gravitational pull, leading to the star's complete collapse into a black hole.

Although the majority of energy liberated during gravitational collapse is radiated rapidly, an external observer never directly witnesses the culmination of this process. Despite the collapse occurring within a finite duration from the perspective of the infalling matter, a remote observer perceives the infalling material as progressively decelerating and appearing to freeze just above the event horizon, a consequence of gravitational time dilation. Photons emitted from the collapsing matter require increasingly extended periods to reach the observer, with this temporal delay approaching infinity as the emitting material approaches the event horizon. Consequently, the event horizon's formation remains unobservable to an external viewer; instead, the collapsing material appears to dim and become progressively red-shifted, ultimately vanishing from sight.

Alternative Formation Mechanisms

The detection of quasars within the first billion years post-Big Bang has prompted research into alternative black hole formation pathways. Given that the accretion process for supermassive black holes has a constrained rate of mass accumulation, a billion-year timeframe is generally considered insufficient for them to achieve quasar luminosity. One hypothesis proposes the direct collapse of primordial, nearly pure hydrogen gas clouds (characterized by low metallicity), prevalent in the early universe, leading to the formation of a supermassive star that subsequently collapses into a black hole. This mechanism could potentially form "seed" black holes with typical masses around ~10⁵ M_☉, which could then accrete further to reach masses of approximately ~10^§1314§ M_☉. Nevertheless, the substantial gas quantities necessary for direct collapse are often gravitationally unstable, prone to fragmentation that would instead yield multiple smaller stars. Consequently, an alternative model posits the formation of massive stars, followed by subsequent collisions that generate seed black holes, which then merge to form a quasar.

A neutron star residing within a common envelope with a companion star may accrete enough mass to undergo collapse into a black hole, or alternatively, two neutron stars could merge to form one. However, these particular pathways for black hole genesis are generally regarded as comparatively infrequent.

Primordial Black Holes and Early Universe Cosmology

In the current cosmic epoch, the requisite conditions for black hole formation are infrequent and primarily confined to stellar interiors. However, the early universe may have facilitated black hole genesis through alternative mechanisms. Spacetime fluctuations shortly after the Big Bang could have generated regions of enhanced density compared to their surroundings. Initially, these regions lacked sufficient compactness for black hole formation, but eventually, the spacetime curvature within them intensified enough to induce gravitational collapse into a black hole. Models describing the early universe exhibit substantial divergence in their predictions regarding the scale of these fluctuations. Various theoretical frameworks forecast the creation of primordial black holes with masses ranging from a Planck mass (approximately 2.2×10⁻⁸ kg) to hundreds of thousands of solar masses. Primordial black holes possessing masses below 10¹² kg would have already evaporated due to Hawking radiation.

Despite the extreme density of the early universe, it did not undergo re-collapse into a black hole during the Big Bang. This is attributed to the universe's rapid expansion and the absence of the necessary gravitational differential for black hole formation. Consequently, models developed for the gravitational collapse of objects with relatively constant dimensions, such as stars, are not directly applicable to rapidly expanding cosmic environments like the Big Bang.

High-Energy Collisions

Theoretically, black holes could emerge from high-energy particle collisions that achieve sufficient density, although no such events have been empirically observed. These hypothetical micro black holes, potentially formed from cosmic ray interactions with Earth's atmosphere or within particle accelerators like the Large Hadron Collider, would be incapable of accumulating additional mass. Instead, they are predicted to evaporate within approximately 10⁻²⁵ seconds, thereby posing no threat to Earth.

Evolution

Following their formation, black holes can undergo transformations through phenomena such as mergers, the accretion of matter, and evaporation via Hawking radiation.

Mergers

Black holes are capable of merging with other celestial bodies, including stars or other black holes. This process is considered crucial, particularly in the early development of supermassive black holes, which may have originated from the aggregation of numerous smaller objects. Mergers have also been proposed as a mechanism for the formation of some intermediate-mass black holes. The coalescence of supermassive black holes can be a protracted process: as a binary system of supermassive black holes approaches, most nearby stars are gravitationally ejected, diminishing the amount of matter available for gravitational interaction that would facilitate further orbital decay. This phenomenon is termed the "final parsec problem," as the critical separation distance is typically around one parsec.

Accretion of Matter

When a black hole accretes matter, the gas within the inner accretion disk orbits at exceptionally high velocities due to its close proximity to the black hole. The resulting frictional forces heat the inner disk to temperatures that induce the emission of vast quantities of electromagnetic radiation, primarily X-rays, which are detectable by telescopes. By the time the disk's matter reaches the innermost stable circular orbit (ISCO), between 5.7% and 42% of its mass will have been converted into energy, a proportion dependent on the black hole's spin. Approximately 90% of this energy is released within 20 black hole radii. In many instances, accretion disks are accompanied by relativistic jets, emitted along the black hole's poles, which dissipate a significant portion of this energy.

Numerous highly energetic cosmic phenomena have been attributed to the accretion of matter onto black holes. Active galactic nuclei and quasars, for example, are powered by accretion onto supermassive black holes. X-ray binaries are widely accepted as binary systems where one compact object accretes matter from its companion star. Furthermore, ultraluminous X-ray sources may represent the accretion disks of intermediate-mass black holes.

At a specific accretion rate, the outward radiation pressure theoretically counterbalances the inward gravitational force, preventing the black hole from accreting matter any faster. This theoretical maximum is known as the Eddington limit. However, many black holes realistically accrete beyond this rate due to factors such as non-spherical geometry or instabilities within the accretion disk. Accretion exceeding this limit is termed super-Eddington accretion and is believed to have been prevalent in the early universe.

Observations have documented instances where stars are gravitationally disrupted by the intense tidal forces near supermassive black holes located in galactic nuclei, a phenomenon termed a tidal disruption event (TDE). A portion of the stellar material subsequently forms an accretion disk around the black hole, generating detectable electromagnetic radiation.

Galactic Interactions

A significant correlation exists between the masses of supermassive black holes residing in galactic centers and the velocity dispersion and stellar mass within their host bulges, indicating an intrinsic relationship between galaxy formation and the development of their central black holes. Rapid accretion can generate black hole winds that compress proximate gas, thereby stimulating star formation, especially during periods when the galaxy itself is actively accreting material. Conversely, excessively powerful winds can expel substantial quantities of gas from the galaxy, effectively suppressing star formation. Furthermore, black hole jets are capable of energizing adjacent plasma cavities and expelling low-entropy gas from the galactic core, resulting in higher-than-anticipated gas temperatures in these central regions.

Black Hole Evaporation

Should Hawking's theory of black hole radiation prove accurate, black holes are predicted to gradually diminish and evaporate over cosmic timescales through the emission of photons and other particles, leading to a loss of mass. The temperature associated with this thermal spectrum, known as the Hawking temperature, is directly proportional to the black hole's surface gravity, which, in turn, is inversely proportional to its mass. Consequently, more massive black holes are theorized to emit less radiation compared to their smaller counterparts. For instance, a stellar black hole with a mass of 1 M_☉ exhibits a Hawking temperature of 62 nanokelvins, a value significantly lower than the 2.7 K temperature of the cosmic microwave background radiation. This implies that black holes of stellar mass or greater would accrete more mass from the cosmic microwave background than they would lose via Hawking radiation, leading to growth rather than shrinkage. For a black hole to possess a Hawking temperature exceeding 2.7 K and thus be capable of evaporation, its mass would need to be less than that of the Moon, corresponding to a diameter under one-tenth of a millimeter.

The Hawking radiation emanating from astrophysical black holes is theoretically anticipated to be extremely faint, rendering its detection from Earth exceptionally challenging. A potential exception involves the microsecond-duration bursts of gamma rays hypothesized to be emitted during the final stages of primordial black hole evaporation. Extensive searches for these predicted flashes have yielded no positive results, thereby imposing stringent constraints on the potential existence of low-mass primordial black holes. Contemporary research suggests that primordial black holes must constitute less than a fraction of 10⁻⁷ of the universe's total mass. The Fermi Gamma-ray Space Telescope, launched by NASA in 2008, has actively sought these flashes but has not yet identified any.

Principles of Black Hole Mechanics and Thermodynamics

Within the framework of general relativity, the fundamental constraints governing a black hole's characteristics are termed the laws of black hole mechanics. For a black hole that is neither actively forming nor accreting matter, the zeroth law of black hole mechanics posits that its surface gravity remains constant across the event horizon. The first law establishes a relationship between alterations in the black hole's surface area, angular momentum, and charge, and corresponding changes in its energy. The second law stipulates that the surface area of a black hole can never spontaneously decrease. Lastly, the third law asserts that a black hole's surface gravity can never reach zero. These principles serve as mathematical analogues to the classical laws of thermodynamics. However, they are not entirely equivalent because, under general relativity without quantum mechanics, a black hole is theorized to be incapable of emitting radiation, implying its temperature must perpetually remain at absolute zero.

Conversely, quantum mechanics predicts that black holes continuously emit thermal Hawking radiation, necessitating a non-zero temperature. Furthermore, it posits that all black holes possess entropy directly proportional to their surface area. When quantum mechanical principles are integrated, the laws of black hole mechanics achieve equivalence with the classical laws of thermodynamics. Nevertheless, these deductions are formulated in the absence of a comprehensive theory of quantum gravity, although numerous theoretical frameworks do anticipate black holes exhibiting both entropy and temperature. Consequently, the precise quantum nature of black hole thermodynamics remains a subject of ongoing scholarly debate.

Observational Evidence

The Milky Way galaxy is theorized to contain millions of black holes originating from stellar collapse. Even smaller galaxies, such as the Draco dwarf galaxy, are estimated to host hundreds of these objects. However, only a limited number of these black holes have been identified to date. Black holes inherently do not emit electromagnetic radiation, with the exception of the hypothetical and typically exceedingly faint Hawking radiation; consequently, astrophysicists must depend on indirect observational evidence to detect them. The event horizon constitutes the definitive feature of a black hole. Since the event horizon itself is not directly observable, all alternative explanations for indirect observations must be thoroughly evaluated and disproven before a definitive conclusion of a black hole's presence can be established.

Direct Interferometry

The Event Horizon Telescope (EHT) represents a global network of radio telescopes designed to directly image the shadow cast by a black hole. A telescope's angular resolution is determined by its aperture size and the wavelengths of radiation it detects. Given the extremely small angular diameters of Sagittarius A* and Messier 87* as observed from Earth, a solitary telescope would require an aperture approximately the size of Earth to distinctly resolve their event horizons at radio wavelengths. The EHT achieves an effective aperture equivalent to Earth's diameter by integrating data from multiple radio telescopes globally. The EHT collaboration employed sophisticated imaging algorithms to reconstruct the most probable images from the observational data pertaining to Sagittarius A* and M87*.

Gravitational Waves

Gravitational-wave interferometry offers a method for detecting the mergers of black holes and other compact astronomical objects. This technique involves splitting a laser beam, directing each component along two extended arms of a tunnel, and subsequently reflecting them back to converge at the arms' intersection, where they are designed to precisely cancel each other out. Nevertheless, the passage of a gravitational wave induces a distortion in spacetime, thereby altering the relative lengths of these interferometer arms. Consequently, as each laser beam traverses a subtly different path length, their cancellation is incomplete, resulting in a detectable signal. Subsequent analysis of this signal provides scientists with insights into the phenomena responsible for generating the gravitational waves. Due to the inherent weakness of gravitational waves, observatories like LIGO necessitate interferometer arms several kilometers in length and rigorous control over terrestrial noise to enable their detection. Since initial measurements commenced in 2016, numerous gravitational waves originating from black hole events have been successfully detected and analyzed.

Stars Orbiting Sagittarius A*

The observed proper motions of stars located in the vicinity of the Milky Way's galactic center furnish compelling observational evidence indicating their orbital trajectories around a supermassive black hole. Astronomers have meticulously monitored the trajectories of 90 stars orbiting an unseen object, which spatially coincides with the radio source Sagittarius A*. Notably, one star, designated S2, has completed a full orbital period. Through the application of Keplerian orbital mechanics to these stellar motions, researchers deduced that the invisible object, presumed to be Sagittarius A*, possesses a mass of approximately 4.3×10⁶ M_☉ and is confined within a radius smaller than 0.002 light-years. This derived upper limit for the radius exceeds the Schwarzschild radius corresponding to the estimated mass, thus this combination alone does not definitively confirm Sagittarius A* as a black hole. Nevertheless, these observations provide robust evidence for the central object being a supermassive black hole, given the absence of other plausible astrophysical mechanisms capable of confining such an immense amount of invisible mass within such a compact volume. Furthermore, luminosity data associated with this object suggests the presence of an event horizon, a fundamental characteristic of black holes. The Event Horizon Telescope's image of Sagittarius A*, published in 2022, offered additional corroboration of its black hole nature.

Binaries

X-ray binaries constitute binary systems primarily characterized by the emission of radiation within the X-ray portion of the electromagnetic spectrum. This X-ray emission originates from the accretion of matter by a compact object from an ordinary stellar companion. The inclusion of an ordinary star within such a system facilitates the investigation of the central object, enabling researchers to ascertain whether it is a black hole. Scientists can estimate the compact object's mass by determining the binary's orbital period, its distance from Earth, and the mass of its companion star. The Tolman-Oppenheimer-Volkoff (TOV) limit defines the maximum mass attainable by a non-rotating neutron star, which is approximated at two solar masses. Although a rotating neutron star may possess a slightly greater mass, a compact object significantly exceeding the TOV limit cannot be a neutron star and is consequently presumed to be a black hole.

Cygnus X-1, identified in 1972 by Charles Thomas Bolton, Louise Webster, and Paul Murdin, represented the initial robust black hole candidate discovered through this methodology. Reports from 1986, based on observations of the optical star's rotational broadening, yielded a compact object mass estimate of 16 solar masses, with a lower bound of 7 solar masses. By 2011, this estimation was refined to 14.1±1.0 M_☉ for the black hole and 19.2±1.9 M_☉ for its optical stellar companion.

X-ray binaries are categorized into either low-mass or high-mass systems, a classification determined by the companion star's mass rather than the compact object's mass. Within the category of soft X-ray transients, a specific type of X-ray binary, the companion star possesses a comparatively low mass, which facilitates more precise estimations of the black hole's mass. These systems exhibit active X-ray emission for only a few months within cycles spanning 10 to 50 years. During periods of reduced X-ray emission, termed quiescence, the accretion disk becomes exceptionally faint, thereby enabling detailed observations of the companion star. This methodology has been employed to measure numerous black hole candidates. Furthermore, black holes are occasionally identified in binary systems alongside other compact objects, including white dwarfs, neutron stars, and other black holes.

Galactic Nuclei

A supermassive black hole resides at the core of almost every galaxy. The M–sigma relation, which describes the strong observational correlation between the mass of this black hole and the velocity dispersion of its host galaxy's bulge, robustly indicates an intrinsic link between the formation processes of the black hole and the galaxy itself.

Active Galactic Nuclei

Astronomers employ the designation active galaxy to characterize galaxies exhibiting anomalous properties, such as atypical spectral line emission and exceptionally potent radio emission. Both theoretical and observational investigations have demonstrated that the intense activity observed in the central regions of these galaxies, known as active galactic nuclei (AGN), can be attributed to accretion onto supermassive black holes. These AGN comprise a central black hole, potentially millions or billions of times more massive than the Sun, an accretion disk composed of interstellar gas and dust, and two jets oriented perpendicularly to the accretion disk.

While supermassive black holes are anticipated in the majority of AGN, only a subset of galactic nuclei has undergone rigorous investigation to identify and quantify the actual masses of central supermassive black hole candidates. Prominent galaxies harboring supermassive black hole candidates include the Andromeda Galaxy, Messier 32, Messier 87, the Sombrero Galaxy, and the Milky Way.

Microlensing

Black holes can also be identified by observing the effects of their intense gravitational fields. Gravitational lensing, for instance, occurs when the spacetime distortion around a massive object deflects light rays, causing background objects to appear distorted. If a black hole acts as the lensing object, this phenomenon can be sufficiently powerful to generate multiple images of a star or other luminous celestial body. Nevertheless, the separation between these lensed images might be too minute for current telescopes to resolve, a phenomenon termed microlensing. In microlensing events, astronomers observe a temporary increase in a star's brightness as a black hole traverses the line of sight between the star and Earth, followed by a return to its original luminosity. The initial three candidate black holes identified through this method were discovered around the year 2000. In January 2022, researchers announced the first confirmed detection and mass measurement of an isolated stellar black hole—one lacking a binary companion—which was identified through microlensing observations conducted by the Hubble Space Telescope.

Key Research Areas

Information Loss Paradox

The no-hair theorem posits that a black hole is characterized solely by three fundamental parameters: its mass, electric charge, and angular momentum. This implies that all other information pertaining to the matter that constituted the black hole is irretrievably lost, as external observation can only ascertain these three properties. Initially, when black holes were believed to be eternal, this apparent information loss posed no significant issue, as the information could be considered to reside within the black hole itself. Nevertheless, black holes gradually dissipate through the emission of Hawking radiation. This radiation, however, does not seem to convey any supplementary information about the black hole's constituent matter, suggesting that this information is permanently obliterated. This phenomenon is known as the black hole information paradox. Theoretical investigations into this paradox have generated both additional paradoxes and novel insights concerning the interplay between quantum mechanics and general relativity. Although a definitive resolution to the paradox remains elusive, ongoing research into this problem is anticipated to be crucial for the development of a theory of quantum gravity.

Supermassive Black Holes in the Early Universe

Astronomical observations of distant galaxies indicate the presence of ultraluminous quasars, fueled by supermassive black holes, in the early universe, extending to redshifts of ${\displaystyle z\geq 7}$. These black holes were initially hypothesized to originate from the gravitational collapse of massive Population III stars. Nevertheless, these stellar remnants lacked sufficient mass to account for the observed early quasars without accreting matter at rates exceeding the Eddington limit, which represents the theoretical maximum rate of black hole accretion.

Physicists have proposed several distinct mechanisms to explain the formation of these supermassive black holes. One hypothesis suggests that smaller black holes could have merged, leading to the formation of the observed supermassive black holes. Alternatively, they might have originated from direct-collapse black holes, where a substantial cloud of hot gas, influenced by low angular momentum or heating from an adjacent galaxy, avoids fragmentation into multiple stars. Under specific conditions, this process could result in the formation of a single supermassive star that collapses directly into a black hole, bypassing conventional stellar evolutionary stages. Furthermore, these early universe supermassive black holes could represent high-mass primordial black holes that subsequently accreted additional matter within galactic centers. Lastly, some proposed mechanisms permit black holes to grow beyond the theoretical Eddington limit, for instance, when dense gas within the accretion disk mitigates the outward radiation pressure that typically inhibits accretion. Nevertheless, the generation of bipolar jets generally impedes sustained super-Eddington accretion rates.

Alternatives to Black Holes

While the existence of supermassive black holes is strongly supported by evidence, the precise demarcation between lighter black holes and neutron stars remains contingent upon theoretical models of matter at extreme densities. Direct observational verification is currently unavailable; consequently, objects exhibiting masses exceeding the theoretical limits for neutron stars are conventionally classified as black holes. Recent findings from gravitational wave events suggest that revisions to these theoretical frameworks may be necessary. The potential existence of novel exotic phases of matter could facilitate the formation of other types of massive celestial bodies. For instance, quark stars would comprise quark matter, sustained by quark degeneracy pressure, a form of degeneracy pressure more potent than neutron degeneracy pressure, thereby arresting gravitational collapse at a mass threshold higher than that for a neutron star. Even more robust, electroweak stars would convert quarks within their cores into leptons, generating additional pressure to counteract stellar collapse. Furthermore, if, as posited by certain extensions of the Standard Model, quarks and leptons are composed of even smaller fundamental particles known as preons, then a highly compact star could be supported by preon degeneracy pressure. Although none of these hypothetical constructs fully account for all observations of stellar black hole candidates, the Q star represents the sole alternative capable of significantly surpassing the mass limit for neutron stars, thus offering a potential alternative explanation for supermassive black holes.

Several theoretical objects have been hypothesized to either precisely or nearly precisely replicate the observational characteristics of astronomical black hole candidates, yet operate through distinct physical mechanisms. A dark energy star, for example, would transform infalling matter into vacuum energy. This internal vacuum energy, significantly greater than that of the surrounding space, would exert outward pressure, thereby preventing the formation of a singularity. A black star is conceived as an object undergoing gravitational collapse at such a protracted rate that quantum effects would maintain it perpetually at the precipice of complete collapse into a black hole. A gravastar, conversely, would consist of an exceedingly thin shell enclosing an interior composed of dark energy, which would provide the necessary outward pressure to avert collapse into a black hole or the formation of a singularity; it could even contain another gravastar internally, termed a 'nestar'.

In fiction

Black holes have been depicted in diverse ways within science fiction narratives. Even prior to the term's coinage, celestial bodies exhibiting characteristics akin to black holes appeared in works such as the 1928 novel The Skylark of Space, featuring a "black Sun," and the "hole in space" described in the 1935 short story Starship Invincible. As black holes gained broader public recognition during the 1960s and 1970s, they became prominent in both cinematic productions and literary works, exemplified by Disney's film The Black Hole. Their presence has continued into 21st-century works, notably Christopher Nolan's science fiction epic Interstellar.

Authors and screenwriters have frequently leveraged the relativistic phenomena associated with black holes, particularly gravitational time dilation. For instance, Interstellar portrays a planet orbiting a black hole where time dilation results in a factor exceeding 60,000:1. Similarly, the 1977 novel Gateway illustrates a spaceship approaching, but never crossing, a black hole's event horizon from an external observer's perspective, due to these time dilation effects. Black holes have also been reinterpreted as wormholes or other conduits for faster-than-light travel, as seen in the 1974 novel The Forever War, where an interconnected network of black holes facilitates interstellar journeys. Furthermore, black holes are often presented as significant hazards to spacefarers and planetary systems. A black hole imperils a deep-space outpost in the 1978 short story The Black Hole Passes, and a binary black hole system dangerously alters a planet's orbit in the 2018 Netflix adaptation of Lost in Space.

References

The Stanford Encyclopedia of Philosophy provides an entry titled "Singularities and Black Holes," authored by Erik Curiel and Peter Bokulich.

• Stanford Encyclopedia of Philosophy: "Singularities and Black Holes" by Erik Curiel and Peter Bokulich.
• Fall Into A Black Hole on Andrew Hamilton's website
• Black Hole News from NASA

The documentary Black Hole Apocalypse, featured on NOVA.

• Black Hole Apocalypse – documentary on NOVA
• A compilation of videos concerning black holes from PBS Space Time.
• A computer-generated visualization depicting a signal detected by LIGO, illustrating gravitational waves produced by merging black holes.
• A realistic simulation depicts the merger of two black holes into a single entity, a phenomenon inferred from the gravitational wave signal GW150914.
• This resource offers a 360-degree NASA simulation accompanied by an explanation of the experience of entering a black hole.