Event horizon

Within the field of astrophysics, an event horizon denotes a spacetime boundary from which no signal can ever propagate to a specified observer. Wolfgang Rindler introduced this term during the 1950s.

In astrophysics, an event horizon is a boundary in spacetime beyond which no signal can ever reach a given observer. Wolfgang Rindler coined the term in the 1950s.

In 1784, John Michell posited that the gravitational force near sufficiently massive compact objects could be so intense as to prevent even light from escaping. During that era, the prevailing scientific frameworks included Newtonian gravitation and the corpuscular theory of light. Within these theoretical constructs, if a massive object's gravitational escape velocity surpassed the speed of light, light emitted from within or from its surface would temporarily escape before being drawn back. Subsequently, in 1958, David Finkelstein employed general relativity to establish a more rigorous definition of a local black hole event horizon. This was conceptualized as a boundary beyond which no event could influence an external observer, thereby generating information and firewall paradoxes that prompted a re-evaluation of local event horizons and the fundamental understanding of black holes. Consequently, various theories emerged, some incorporating event horizons and others not. Stephen Hawking, a prominent theorist in black hole physics, proposed substituting the event horizon with an apparent horizon, stating, "Gravitational collapse produces apparent horizons but no event horizons." Ultimately, he concluded that "the absence of event horizons means that there are no black holes – in the sense of regimes from which light cannot escape to infinity."

An object approaching the horizon from an observer's perspective will appear to decelerate, never definitively traversing the boundary. Concurrently, gravitational redshift causes its visual spectrum to shift towards red as the object nears the horizon.

Within an expanding universe, the rate of expansion can attain, and even surpass, the speed of light, thereby precluding signals from reaching certain cosmic regions. A cosmic event horizon constitutes a genuine event horizon, as its influence extends to all forms of signals, including gravitational waves, which propagate at the speed of light.

More specialized categories of horizons encompass the absolute and apparent horizons, which are related yet distinct phenomena observed in the vicinity of black holes. Additional distinct classifications comprise:

• The Cauchy and Killing horizons.
• The photon spheres and ergospheres associated with the Kerr solution.
• Particle and cosmological horizons, which are pertinent to the study of cosmology.
• Isolated and dynamical horizons, both of which hold significant importance in contemporary black hole research.

The Cosmic Event Horizon

Within cosmology, the event horizon of the observable universe is defined as the maximum comoving distance from which light emitted at the present moment can ultimately reach an observer in the future. This concept diverges from the particle horizon, which denotes the greatest comoving distance from which light emitted in the past could have reached an observer by a specific epoch. Events originating beyond this distance remain unobservable, as light has not had sufficient time to traverse the intervening space to our location, even if emitted at the universe's inception. The temporal evolution of the particle horizon is contingent upon the characteristics of cosmic expansion. Should the expansion exhibit particular properties, certain regions of the universe will perpetually remain unobservable, irrespective of the duration an observer might wait for light from those areas. The ultimate boundary beyond which events can never be observed constitutes an event horizon, signifying the maximal reach of the particle horizon.

The criterion for ascertaining the existence of a particle horizon for the universe is articulated as follows: A comoving distance, denoted as d_p, is defined as:

d p = ∫<!-- ∫ --> §2122§ t §2930§ c a ( t ) d t . {\displaystyle d_{p}=\int _{0}^{t_{0}}{\frac {c}{a(t)}}\,dt.}

This equation defines a as the scale factor, c as the speed of light, and t§67§ as the Universe's age. An event horizon is absent if d_p → ∞, indicating points are infinitely distant and observable. Conversely, a horizon is present when d_p ≠ ∞.

Cosmological models lacking an event horizon include universes primarily composed of matter or radiation. In contrast, a universe dominated by the cosmological constant, known as a de Sitter universe, exemplifies a model that features an event horizon.

A scholarly publication concerning the FLRW cosmological model presented calculations for the velocities of cosmological event and particle horizons, based on an approximation of the Universe as comprising non-interacting constituents, each behaving as a perfect fluid.

The Apparent Horizon of an Accelerated Particle

In a non-expanding, gravity-free universe, a particle moving at a constant velocity will eventually observe any event, as the forward light cones from these events intersect its world line. However, if the particle undergoes acceleration, certain light cones may never intersect its world line. In such scenarios, an apparent horizon emerges within the particle's accelerating reference frame, delineating a boundary beyond which events remain unobservable.

This phenomenon is exemplified by a uniformly accelerated particle. Its spacetime diagram illustrates a hyperbolic trajectory that asymptotically approaches a 45-degree line, representing a light ray's path. As the particle accelerates, it approaches, but never attains, the speed of light relative to its initial reference frame. Consequently, any event whose light cone's edge coincides with or extends beyond this asymptote remains unobservable to the accelerating particle. Within the particle's reference frame, an apparent horizon forms behind it, preventing the escape of any signals. The distance to this boundary is defined by ${\displaystyle c^{2}/a}$, where a denotes the particle's constant proper acceleration.

Although real-world scenarios, such as those in particle accelerators, can approximate this situation, a genuine event horizon never forms. Its formation would necessitate indefinite particle acceleration, demanding arbitrarily vast energy inputs and an apparatus of unbounded size.

Interaction with a Cosmic Horizon

For a uniformly accelerating observer in empty space, the perceived horizon maintains a constant distance, irrespective of the motion of its environment. Adjustments to the observer's acceleration can induce apparent movement of the horizon over time or, depending on the specific acceleration function, preclude the existence of an event horizon entirely. The observer neither physically contacts the horizon nor traverses its apparent location.

Within a de Sitter universe, a non-accelerating observer consistently perceives the horizon at a fixed distance. This horizon remains uncontacted, even by an observer undergoing acceleration.

The Event Horizon of a Black Hole

A prominent illustration of an event horizon originates from general relativity's characterization of a black hole: a celestial body of such immense density that neither proximate matter nor radiation can escape its gravitational influence. While frequently defined as the boundary where the black hole's escape velocity exceeds the speed of light, a more precise explanation posits that within this horizon, all lightlike trajectories—and consequently all paths within the forward light cones of particles—are distorted, leading them further into the black hole. Once a particle crosses this horizon, its progression into the black hole becomes as inescapable as advancing through time, regardless of its direction of travel, and can be considered analogous, contingent upon the chosen spacetime coordinate system.

The Schwarzschild radius defines the event horizon for a non-rotating celestial body that collapses within this specific radius; rotating black holes exhibit slightly different characteristics. This radius is directly proportional to an object's mass. Theoretically, any quantity of matter would form a black hole if compressed sufficiently to fit within its calculated Schwarzschild radius. For instance, the Sun's Schwarzschild radius is approximately 3 kilometers (1.9 miles), while Earth's is about 9 millimeters (0.35 inches). However, neither Earth nor the Sun possesses the requisite mass and gravitational force to overcome the electron and neutron degeneracy pressures that prevent such a collapse. The minimum stellar mass necessary to surmount these pressures and undergo gravitational collapse is known as the Tolman–Oppenheimer–Volkoff limit, which is approximately three solar masses.

Fundamental models of gravitational collapse indicate that an event horizon precedes the formation of a black hole's singularity. Should all stars within the Milky Way progressively converge towards the galactic center, maintaining their relative distances, they would collectively fall within their combined Schwarzschild radius well before any physical collisions occur. Until such a distant future collapse, observers residing within a galaxy enveloped by an event horizon would continue their existence without immediate disruption.

The nature of black hole event horizons is frequently misinterpreted. A prevalent, yet incorrect, belief posits that black holes actively "vacuum" nearby material; however, they possess no greater capacity to attract matter than any other gravitational body. Analogous to any mass in the cosmos, material must enter a black hole's gravitational field for capture or accretion to occur. Another common misconception is the direct observation of matter falling into a black hole, which is unfeasible. Astronomers can only detect accretion disks surrounding black holes, where the high velocity of orbiting material generates intense frictional forces, producing detectable high-energy radiation. Concurrently, some matter from these accretion disks is ejected along the black hole's rotational axis, forming visible jets when interacting with interstellar gas or when directed towards Earth. Moreover, a remote observer would never witness an object actually crossing the event horizon. Instead, as an object approaches the black hole, its apparent motion would progressively slow, and any emitted light would undergo increasing redshift.

Alternatively, the event horizon can be characterized by the causal structure of spacetime. Trajectories intersecting a specific point in spacetime are constrained to paths within a light cone, dictated by the speed of light. Spacetime curvature influences the orientation of these light cones. At a black hole's event horizon, the curvature intensifies to such a degree that all possible paths lead exclusively towards the black hole, with no escape routes.

From a topological perspective, the event horizon is defined by the causal structure as the past null cone of future conformal timelike infinity. A black hole's event horizon possesses a teleological character, implying its determination by future events. More precisely, ascertaining the existence of an event horizon would necessitate knowledge of the universe's complete history extending into the infinite future, a feat unattainable for quasilocal observers, even in principle. Consequently, no experiment or measurement conducted within a finite spacetime region and finite time interval can definitively confirm the presence of an event horizon. Due to this inherently theoretical definition, an object traversing the event horizon does not necessarily encounter unusual phenomena and, in its own proper time, crosses this calculated boundary within a finite duration.

Interactions with Black Hole Event Horizons

A common misconception regarding event horizons, particularly those associated with black holes, posits them as an unyielding boundary that annihilates approaching objects. However, from the perspective of any external observer, all event horizons consistently appear to be situated at a finite distance. Objects directed towards an event horizon are never observed to traverse it from the sending observer's viewpoint, primarily because the light cone of the horizon-crossing event never intersects the observer's world line. Furthermore, maintaining an object in a stationary position relative to an observer near the horizon necessitates the application of a force that increases infinitely as the object approaches the horizon.

For a black hole's event horizon, observers who remain stationary relative to a distant object will concur on its precise location. Although this might suggest that an observer could be lowered on a rope or rod to make contact with the horizon, this is practically infeasible. While the proper distance to the horizon is finite, implying a finite rope length, a slow descent (where each point on the rope is approximately at rest in Schwarzschild coordinates) would subject points closer to the horizon to proper accelerations (G-forces) that approach infinity, inevitably causing the rope to rupture. Conversely, if the rope is lowered rapidly, potentially even in freefall, the observer at its end could indeed touch and even cross the event horizon. However, once this occurs, retrieving the rope's lower section from beyond the event horizon becomes impossible. If the rope is pulled taut, the forces along it would increase without bound as they near the event horizon, leading to an inevitable break. Crucially, this rupture would occur not at the event horizon itself, but at a point observable by the second, external observer.

Assuming the potential apparent horizon is situated significantly within the event horizon, or is absent entirely, observers traversing a black hole's event horizon would not perceive or experience any immediate, distinct phenomena. Visually, an observer falling into the black hole would eventually perceive the apparent horizon as an opaque, black region encompassing the singularity. Other objects that previously entered the horizon region along the same radial trajectory would remain visible below the observer, provided they have not yet crossed the apparent horizon, allowing for potential communication. Locally, increasing tidal forces become noticeable, their magnitude being a function of the black hole's mass. In the context of realistic stellar black holes, spaghettification—the tearing apart of material by tidal forces—occurs well before reaching the event horizon. Conversely, within supermassive black holes, typically located at galactic centers, spaghettification manifests inside the event horizon. Consequently, a human astronaut could only survive the passage through an event horizon if the black hole possesses a mass of approximately 10,000 solar masses or more.

Beyond General Relativity

While a cosmic event horizon is generally accepted as a genuine physical boundary, the characterization of a local black hole event horizon provided by general relativity is considered both incomplete and contentious. When the circumstances leading to local event horizons are analyzed through a more comprehensive cosmological framework, one that integrates both relativity and quantum mechanics, these local event horizons are anticipated to exhibit properties distinct from those predicted solely by general relativity.

Currently, the Hawking radiation mechanism posits that the primary influence of quantum effects on event horizons is the acquisition of a temperature, leading to the emission of radiation. In the context of black holes, this phenomenon is known as Hawking radiation, and the broader inquiry into how black holes acquire a temperature forms a central aspect of black hole thermodynamics. For accelerating particles, this quantum effect manifests as the Unruh effect, which causes the surrounding space to appear populated with matter and radiation.

The controversial black hole firewall hypothesis proposes that matter infalling into a black hole would be incinerated by a high-energy "firewall" located at the event horizon.

The complementarity principle offers an alternative perspective, positing that from the viewpoint of a distant observer, infalling matter undergoes thermalization at the horizon and is subsequently reemitted as Hawking radiation. Conversely, an observer falling into the black hole would perceive matter traversing the inner region unimpeded until its destruction at the singularity. This hypothesis aligns with the no-cloning theorem, as only one copy of the information exists from any specific observer's frame of reference. Furthermore, black hole complementarity is supported by the scaling behaviors of strings as they approach the event horizon, indicating that within the Schwarzschild coordinate system, these strings extend to encompass the horizon and thermalize into a membrane with Planck-length thickness.

A comprehensive understanding of local event horizons, which are generated by gravitational forces, necessitates, at a minimum, the development of a quantum gravity theory. M-theory represents one potential candidate for such a theory, while loop quantum gravity offers another promising theoretical framework.

Abraham–Lorentz force

• Abraham–Lorentz force
• Acoustic metric
• Beyond black holes
• Black hole electron
• Black hole starship
• Cosmic censorship hypothesis
• Dynamical horizon
• Event Horizon Telescope
• Hawking radiation
• Kugelblitz (astrophysics)
• Micro black hole
• Rindler coordinates

Notes

References

Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation (27th printing ed.). New York, NY: Freeman. ISBN 978-0-7167-0344-0.

• Misner, Charles W.; Thorne, Kip S.; Wheeler, John Archibald (1973). Gravitation (27. printing ed.). New York, NY: Freeman. ISBN 978-0-7167-0344-0.Hawking, Stephen W. (2001). The Universe in a Nutshell. New York: Bantam. ISBN 978-0-553-80202-3.Thorne, Kip S. (1994). Black Holes and Time Warps: Einstein's Outrageous Legacy. The Commonwealth Fund Book Program. New York / London: Norton. ISBN 978-0-393-31276-8.Ashtekar, Abhay; Krishnan, Badri (2004). "Isolated and Dynamical Horizons and Their Applications". Living Reviews in Relativity. 7 (1): 10. arXiv:gr-qc/0407042. Bibcode:2004LRR.....7...10A. doi:10.12942/lrr-2004-10. ISSN 2367-3613. PMC 5253930. PMID 28163644.Source: TORIma Academy Archive