Event horizon

# Event horizon

Overview
In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, an event horizon is a boundary in spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case of an event horizon is that surrounding a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

. Light emitted from beyond the horizon can never reach the observer. Likewise, any object approaching the horizon from the observer's side appears to slow down and never quite pass through the horizon, with its image becoming more and more redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...

ed as time elapses. The traveling object, however, experiences no strange effects and does, in fact, pass through the horizon in a finite amount of proper time
Proper time
In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...

.
Discussion

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Encyclopedia
In general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

, an event horizon is a boundary in spacetime
Spacetime
In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space as being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions...

beyond which events cannot affect an outside observer. In layman's terms it is defined as "the point of no return" i.e. the point at which the gravitational pull becomes so great as to make escape impossible. The most common case of an event horizon is that surrounding a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

. Light emitted from beyond the horizon can never reach the observer. Likewise, any object approaching the horizon from the observer's side appears to slow down and never quite pass through the horizon, with its image becoming more and more redshift
Redshift
In physics , redshift happens when light seen coming from an object is proportionally increased in wavelength, or shifted to the red end of the spectrum...

ed as time elapses. The traveling object, however, experiences no strange effects and does, in fact, pass through the horizon in a finite amount of proper time
Proper time
In relativity, proper time is the elapsed time between two events as measured by a clock that passes through both events. The proper time depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a smaller elapsed time between two...

.

More specific types of horizon include the related but distinct absolute
Absolute horizon
In general relativity, an absolute horizon is a boundary in spacetime, defined with respect to the external universe, inside of which events cannot affect an external observer. Light emitted inside the horizon can never reach the observer, and anything that passes through the horizon from the...

and apparent horizon
Apparent horizon
In general relativity, an apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards, and those directed outwards but moving inwards.Apparent horizons are not invariant properties of a spacetime...

s found around a black hole. Still other distinct notions include the Cauchy
Cauchy horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem...

and Killing horizon
Killing horizon
A Killing horizon is a null hypersurface on which there is a null Killing vector field .Associated to a Killing horizon is a geometrical quantity known as surface gravity, \kappa...

; the photon spheres and ergosphere
Ergosphere
The ergosphere is a region located outside a rotating black hole. Its name is derived from the Greek word ergon, which means “work”. It received this name because it is theoretically possible to extract energy and mass from the black hole in this region...

s of the Kerr solution; particle and cosmological horizons relevant to cosmology
Cosmology
Cosmology is the discipline that deals with the nature of the Universe as a whole. Cosmologists seek to understand the origin, evolution, structure, and ultimate fate of the Universe at large, as well as the natural laws that keep it in order...

; and isolated and dynamical horizons important in current black hole research.

## Event horizon of a black hole

 Far away from the black hole a particle can move in any direction. It is only restricted by the speed of light. Closer to the black hole spacetime starts to deform. In some convenient coordinate systems, there are more paths going towards the black hole than paths moving away. Inside of the event horizon all paths bring the particle closer to the center of the black hole. It is no longer possible for the particle to escape.

One of the most well-known examples of an event horizon derives from general relativity's description of a black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

, a celestial object so dense that no nearby matter or radiation can escape its gravitational field
Gravitational field
The gravitational field is a model used in physics to explain the existence of gravity. In its original concept, gravity was a force between point masses...

. Often, this is described as the boundary within which the black hole's escape velocity
Escape velocity
In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero gravitational potential energy is negative since gravity is an attractive force and the potential is defined to be zero at infinity...

is greater than the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

. However, a more accurate description is that within this horizon, all lightlike paths (paths that light could take) and hence all paths in the forward light cone
Light cone
A light cone is the path that a flash of light, emanating from a single event and traveling in all directions, would take through spacetime...

s of particles within the horizon, are warped so as to fall farther into the hole. Once a particle is inside the horizon, moving into the hole is as inevitable as moving forward in time, and can actually be thought of as equivalent to doing so, depending on the spacetime coordinate system used.

The surface at the Schwarzschild radius
The Schwarzschild radius is the distance from the center of an object such that, if all the mass of the object were compressed within that sphere, the escape speed from the surface would equal the speed of light...

acts as an event horizon in a non-rotating body that fits inside this radius (although a rotating black hole
Rotating black hole
A rotating black hole is a black hole that possesses spin angular momentum.-Types of black holes:There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate...

operates slightly differently). The Schwarzschild radius of an object is proportional to its mass. Theoretically, any amount of matter will become a black hole if compressed into a space that fits within its corresponding Schwarzschild radius. For the mass of the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

this radius is approximately 3 kilometers and for the Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...

it is about 9 millimeters. In practice, however, neither the Earth nor the Sun has the necessary mass and therefore the necessary gravitational force, to overcome electron
Electron degeneracy pressure
Electron degeneracy pressure is a particular manifestation of the more general phenomenon of quantum degeneracy pressure. The Pauli Exclusion Principle disallows two half integer spin particles from occupying the same quantum state at a given time. The resulting emergent repulsive force is...

and neutron degeneracy pressure. The minimal mass required for a star to be able to collapse beyond these pressures is the Tolman-Oppenheimer-Volkoff limit
Tolman-Oppenheimer-Volkoff limit
The Tolman–Oppenheimer–Volkoff limit is an upper bound to the mass of stars composed of neutron-degenerate matter . The TOV limit is analogous to the Chandrasekhar limit for white dwarf stars.-History:...

, which is approximately three solar masses.

Black hole event horizons are especially noteworthy for three reasons. First, there are many examples near enough to study. Second, black holes tend to pull in matter from their environment, which provides examples where matter about to pass through an event horizon is expected to be observable. Third, the description of black holes given by general relativity is known to be an approximation and it is expected that quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

effects become significant in the vicinity of the event horizon. This allows observations of matter in the vicinity of a black hole's event horizon to be used to indirectly study general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

and proposed extensions to it.

## Particle horizon of the observable universe

The particle horizon of the observable universe
Observable universe
In Big Bang cosmology, the observable universe consists of the galaxies and other matter that we can in principle observe from Earth in the present day, because light from those objects has had time to reach us since the beginning of the cosmological expansion...

is the boundary that represents the maximum distance at which events can currently be observed. For events beyond that distance, light has not had time to reach our location, even if it were emitted at the time the universe began. How the particle horizon changes with time depends on the nature of the expansion of the universe. If the expansion has certain characteristics, there are parts of the universe that will never be observable, no matter how long the observer waits for light from those regions to arrive. The boundary past which events cannot ever be observed is an event horizon, and it represents the maximum extent of the particle horizon.

The criterion for determining whether an event horizon for the universe exists is as follows. Define a comoving distance
Comoving distance
In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects...

by

In this equation, a is the scale factor
Scale factor (Universe)
The scale factor or cosmic scale factor parameter of the Friedmann equations is a function of time which represents the relative expansion of the universe. It is sometimes called the Robertson-Walker scale factor...

, c is the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...

, and t0 is the age of the universe. If (i.e. points arbitrarily as far away as can be observed), then no event horizon exists. If , a horizon is present.

Examples of cosmological models without an event horizon are universes dominated by matter
Matter
Matter is a general term for the substance of which all physical objects consist. Typically, matter includes atoms and other particles which have mass. A common way of defining matter is as anything that has mass and occupies volume...

Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

. An example of a cosmological model with an event horizon is a universe dominated by the cosmological constant
Cosmological constant
In physical cosmology, the cosmological constant was proposed by Albert Einstein as a modification of his original theory of general relativity to achieve a stationary universe...

(a de Sitter universe
De Sitter universe
A de Sitter universe is a cosmological solution to Einstein's field equations of General Relativity which is named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to...

).

## Apparent horizon of an accelerated particle

If a particle is moving at a constant velocity in a non-expanding universe free of gravitational fields, any event that occurs in that universe will eventually be observable by the particle, because the forward light cone
Light cone
A light cone is the path that a flash of light, emanating from a single event and traveling in all directions, would take through spacetime...

s from these events intersect the particle's world line
World line
In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" by the time dimension, and typically encompasses a large area of spacetime wherein...

. On the other hand, if the particle is accelerating, in some situations light cones from some events never intersect the particle's world line. Under these conditions, an apparent horizon
Apparent horizon
In general relativity, an apparent horizon is a surface that is the boundary between light rays that are directed outwards and moving outwards, and those directed outwards but moving inwards.Apparent horizons are not invariant properties of a spacetime...

is present in the particle's (accelerating) reference frame, representing a boundary beyond which events are unobservable.

For example, this occurs with a uniformly accelerated particle. A space-time diagram of this situation is shown in the figure to the right. As the particle accelerates, it approaches, but never reaches, the speed of light with respect to its original reference frame. On the space-time diagram, its path is a hyperbola
Hyperbola
In mathematics a hyperbola is a curve, specifically a smooth curve that lies in a plane, which can be defined either by its geometric properties or by the kinds of equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, which are mirror...

, which asymptotically approaches
Asymptote
In analytic geometry, an asymptote of a curve is a line such that the distance between the curve and the line approaches zero as they tend to infinity. Some sources include the requirement that the curve may not cross the line infinitely often, but this is unusual for modern authors...

a 45 degree line (the path of a light ray). An event whose light cone's edge is this asymptote or is farther away than this asymptote can never be observed by the accelerating particle. In the particle's reference frame, there appears to be a boundary behind it from which no signals can escape (an apparent horizon).

While approximations of this type of situation can occur in the real world (in particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s, for example), a true event horizon is never present, as the particle must be accelerated indefinitely (requiring arbitrarily large amounts of energy and an arbitrarily large apparatus).

## Interacting with an event horizon

A misconception concerning event horizons, especially black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

event horizons, is that they represent an immutable surface that destroys objects that approach them. In practice, all event horizons appear to be some distance away from any observer, and objects sent towards an event horizon never appear to cross it from the sending observer's point of view (as the horizon-crossing event's light cone
Light cone
A light cone is the path that a flash of light, emanating from a single event and traveling in all directions, would take through spacetime...

never intersects the observer's world line
World line
In physics, the world line of an object is the unique path of that object as it travels through 4-dimensional spacetime. The concept of "world line" is distinguished from the concept of "orbit" or "trajectory" by the time dimension, and typically encompasses a large area of spacetime wherein...

). Attempting to make an object near the horizon remain stationary with respect to an observer requires applying a force whose magnitude increases unbounded (becoming infinite) the closer it gets.

For the case of a horizon perceived by a uniformly accelerating observer in empty space, the horizon seems to remain a fixed distance from the observer no matter how its surroundings move. Varying the observer's acceleration may cause the horizon to appear to move over time, or may prevent an event horizon from existing, depending on the acceleration function chosen. The observer never touches the horizon and never passes a location where it appeared to be.

For the case of a horizon perceived by an occupant of a De Sitter Universe
De Sitter universe
A de Sitter universe is a cosmological solution to Einstein's field equations of General Relativity which is named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are dominated by the cosmological constant, thought to...

, the horizon always appears to be a fixed distance away for a non-accelerating
Inertial frame of reference
In physics, an inertial frame of reference is a frame of reference that describes time homogeneously and space homogeneously, isotropically, and in a time-independent manner.All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not...

observer. It is never contacted, even by an accelerating observer.

For the case of the horizon around a black hole, observers stationary with respect to a distant object will all agree on where the horizon is. While this seems to allow an observer lowered towards the hole on a rope (or rod) to contact the horizon, in practice this cannot be done. The proper distance to the horizon is finite, so the length of rope needed would be finite as well, but if the rope was lowered slowly (so that each point on the rope was approximately at rest in Schwarzschild coordinates
Schwarzschild coordinates
In the theory of Lorentzian manifolds, spherically symmetric spacetimes admit a family of nested round spheres. In such a spacetime, a particularly important kind of coordinate chart is the Schwarzschild chart, a kind of polar spherical coordinate chart on a static and spherically symmetric...

), the proper acceleration
Proper acceleration
In relativity theory, proper acceleration is the physical acceleration experienced by an object. It is acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured...

(G-force) experienced by points on the rope closer and closer to the horizon would approach infinity, so the rope would be torn apart. If the rope is lowered quickly (perhaps even in freefall), then indeed the observer at the bottom of the rope can touch and even cross the event horizon. But once this happens it is impossible to pull the bottom of rope back out of the event horizon, since if the rope is pulled taut, the forces along the rope increase without bound as they approach the event horizon and at some point the rope must break. Furthermore, the break must occur not at the event horizon, but at a point where the second observer can observe it.

An observer crossing a black hole event horizon can calculate the moment they've crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon. Other objects that had entered the horizon along the same radial path but at an earlier time would appear below the observer but still above the visual position of the horizon, and if they had fallen in recently enough the observer could exchange messages with them before either one was destroyed by the gravitational singularity
Gravitational singularity
A gravitational singularity or spacetime singularity is a location where the quantities that are used to measure the gravitational field become infinite in a way that does not depend on the coordinate system...

. Increasing tidal force
Tidal force
The tidal force is a secondary effect of the force of gravity and is responsible for the tides. It arises because the gravitational force per unit mass exerted on one body by a second body is not constant across its diameter, the side nearest to the second being more attracted by it than the side...

s (and eventual impact with the hole's singularity) are the only locally noticeable effects.

## Beyond general relativity

The description of event horizons given by general relativity
General relativity
General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1916. It is the current description of gravitation in modern physics...

is thought to be incomplete. When the conditions under which event horizons occur are modeled using a more comprehensive picture of the way the universe works, that includes both relativity and quantum mechanics
Quantum mechanics
Quantum mechanics, also known as quantum physics or quantum theory, is a branch of physics providing a mathematical description of much of the dual particle-like and wave-like behavior and interactions of energy and matter. It departs from classical mechanics primarily at the atomic and subatomic...

, event horizons are expected to have properties that are different from those predicted using general relativity alone.

At present, it is expected that the primary impact of quantum effects is for event horizons to possess a temperature
Temperature
Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

and so emit radiation. For black hole
Black hole
A black hole is a region of spacetime from which nothing, not even light, can escape. The theory of general relativity predicts that a sufficiently compact mass will deform spacetime to form a black hole. Around a black hole there is a mathematically defined surface called an event horizon that...

s, this manifests as Hawking radiation
Hawking radiation is a thermal radiation with a black body spectrum predicted to be emitted by black holes due to quantum effects. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974, and sometimes also after the physicist Jacob Bekenstein...

, and the larger question of how the black hole possesses a temperature is part of the topic of black hole thermodynamics
Black hole thermodynamics
In physics, black hole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of black hole event horizons...

. For accelerating particles, this manifests as the Unruh effect
Unruh effect
The Unruh effect , was first described by Stephen Fulling in 1973, Paul Davies in 1975 and Bill Unruh in 1976. It is the prediction that an accelerating observer will observe black-body radiation where an inertial observer would observe none...

, which causes space around the particle to appear to be filled with matter and radiation.

A complete description of event horizons is expected to, at minimum, require a theory of quantum gravity
Quantum gravity
Quantum gravity is the field of theoretical physics which attempts to develop scientific models that unify quantum mechanics with general relativity...

. One such candidate theory is M-theory
M-theory
In theoretical physics, M-theory is an extension of string theory in which 11 dimensions are identified. Because the dimensionality exceeds that of superstring theories in 10 dimensions, proponents believe that the 11-dimensional theory unites all five string theories...

. Another such candidate theory is Loop Quantum Gravity
Loop quantum gravity
Loop quantum gravity , also known as loop gravity and quantum geometry, is a proposed quantum theory of spacetime which attempts to reconcile the theories of quantum mechanics and general relativity...

.