In general relativity General relativity or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a geometric property of space and time, or spacetime, an event horizon is a boundary in spacetime In physics, spacetime is any mathematical model that combines space and time into a single continuum. Spacetime is usually interpreted with space being three-dimensional and time playing the role of a fourth dimension that is of a different sort from the spatial dimensions. According to certain Euclidean space perceptions, the universe has three, most often an area surrounding a black hole A black hole, according to the general theory of relativity, is a region of space from which nothing, including light, can escape. It is the result of the deformation of spacetime caused by a very compact mass. Around a black hole there is an undetectable surface which marks the point of no return, called an event horizon. It is called "black&, beyond which events cannot affect an outside observer. Light emitted from beyond the horizon can never reach the observer, and any object that approaches 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 redshifted In physics , redshift happens when light seen coming from an object is proportionally shifted to appear more red. Here, the term "redder" refers to what happens when visible light is shifted toward the red end of the visible spectrum. More generally, where an observer detects electromagnetic radiation outside the visible spectrum, " 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 In relativity, proper time is time measured by a single clock between events that occur at the same place as the clock. It depends not only on the events but also on the motion of the clock between the events. An accelerated clock will measure a proper time between two events that is shorter than the coordinate time measured by a non-accelerated.

More specific types of horizon include the related but distinct absolute 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 observer's side is never seen again. An absolute and apparent horizons An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards found around a black hole. Still other distinct notions include the Cauchy In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem . One side of the horizon contains closed space-like geodesics and the other side contains closed time-like geodesics and Killing horizon Exact black hole metrics such as the Kerr-Newman metric contain Killing horizons which coincide with their event horizons. It should be emphasized, however, that these two notions of horizon are independent. For this spacetime, the Killing horizon is located at; the photon spheres A photon sphere is a spherical region of space where gravity is strong enough that photons are forced to travel in orbits. The formula to find the radius for a circular photon orbit is: r=3GM/C2. Because of this equation photon spheres can only exist in the space surrounding an extremely compact object, such as a black hole and ergospheres 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 of the Reissner-Nordström solution In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein field equations in empty space, which corresponds to the gravitational field of a charged, non-rotating, spherically symmetric body of mass M; particle In physical cosmology, particle horizon is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the portion of the universe which we could have conceivably observed at the present day. In other words, the particle horizon represents a boundary between the observable and and cosmological horizons In physical cosmology, a cosmological horizon is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the boundary between the portion of the universe which could have conceivably been observed at a given time (the observable universe) and the unobservable regions of the universe relevant to cosmology Cosmology , in strict usage, refers to the study of the Universe in its totality as it now is (or at least as it can be observed now), and by extension, humanity's place in it. Though the word cosmology is recent (first used in 1730 in Christian Wolff's Cosmologia Generalis), study of the universe has a long history involving science, philosophy,; and isolated and dynamical horizons important in current black hole research.

Event horizon of a black hole

The most commonly known example of an event horizon is defined around general relativity's description of a black hole A black hole, according to the general theory of relativity, is a region of space from which nothing, including light, can escape. It is the result of the deformation of spacetime caused by a very compact mass. Around a black hole there is an undetectable surface which marks the point of no return, called an event horizon. It is called "black&, a celestial object so dense that no matter or radiation can escape its gravitational field A gravitational field is a model used within physics to explain how gravity exists in the universe. In its original concept, gravity was a force between point masses. Following Newton, Laplace attempted to model gravity as some kind of radiation field or fluid, and since the 19th century explanations for gravity have usually been sought in terms. This is sometimes described as the boundary within which the black hole's escape velocity In physics, escape velocity is the speed at which the kinetic energy plus the gravitational potential energy of an object is zero. It is commonly described as the speed needed to "break free" from a gravitational field. The term escape velocity is actually a misnomer, as the concept refers to a scalar speed which is independent of is greater than the speed of light The speed of light, usually denoted by c, is a physical constant, so named because it is the speed at which light and all other electromagnetic radiation travels in vacuum. Its value is exactly 299,792,458 metres per second, often approximated as 300,000 kilometres per second or 186,000 miles per second. In the theory of relativity, c connects. A more accurate description is that within this horizon, all lightlike In physics and mathematics, Minkowski space is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime. Minkowski space is named paths (paths that light could take) and hence all paths in the forward light cones A light cone is the path that a flash of light, emanating from a single event E and traveling in all directions, would take through spacetime. If we imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph 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 a characteristic radius associated with every quantity of mass. It is the radius of a sphere in space, that if containing a correspondingly sufficient amount of mass (and therefore, reaches a certain density), the force of gravity from the contained mass would be so great that no known force or degeneracy pressure could acts as an event horizon in a non-rotating body that fits inside this radius (A rotating black hole There are four known, exact, black hole solutions to Einstein's equations, which describe gravity in General Relativity. Two of these rotate. It is generally believed that all black holes will eventually be similar to a stationary black hole and, by the no hair theorem, that stationary black holes can be completely described by three (and only 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 The Sun is the star at the center of the Solar System. It has a diameter of about 1,392,000 kilometers , about 109 times that of Earth, and its mass (about 2 × 1030 kilograms, 330,000 times that of Earth) accounts for about 99.86% of the total mass of the Solar System. About three quarters of the Sun's mass consists of hydrogen, while the rest is this radius is approximately 3 kilometers and for the 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 sometimes referred to as the World, the Blue Planet,[note 6] or by its Latin name, Terra.[note 7] 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 is a consequence of the Pauli exclusion principle, which states that two fermions cannot occupy the same quantum state at the same time. The force provided by this pressure sets a limit on the extent to which matter can be squeezed together without it collapsing into a neutron star or black hole. It is an important 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 The Tolman–Oppenheimer–Volkoff limit is an upper bound to the mass of stars composed of neutron-degenerate matter (i.e. neutron stars). It is analogous to the Chandrasekhar limit for white dwarf stars, 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 is the field of theoretical physics attempting to unify quantum mechanics with general relativity in a self-consistent manner, or more precisely, to formulate a self-consistent theory which reduces to ordinary quantum mechanics in the limit of weak gravity (potentials much less than c2) and which reduces to Einsteinian general 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 or the general theory of relativity is the geometric theory of gravitation published by Albert Einstein in 1915. It is the current description of gravitation in modern physics. It unifies special relativity and Newton's law of universal gravitation, and describes gravity as a geometric property of space and time, or spacetime and proposed extensions to it.

The definition of "event horizon" given by Hawking & Ellis,^[1] Misner, Thorne & Wheeler,^[2] and Wald^[3] differs from the one presented here. Their definition rules out the cosmological and particle horizons presented below (as well as the apparent horizon An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards). However, modern usage has brought those ideas under the umbrella of the term "event horizon".^[4] To make the distinction clearer, some authors refer to their more specific notion of a horizon as an "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 observer's side is never seen again. An absolute". In the context of black holes, event horizon almost always refers to the absolute horizon, as distinct from the apparent horizon.

Event horizon of the observable universe

The particle horizon In physical cosmology, particle horizon is the maximum distance from which particles could have traveled to the observer in the age of the universe. It represents the portion of the universe which we could have conceivably observed at the present day. In other words, the particle horizon represents a boundary between the observable and of the 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. Assuming the Universe is isotropic, the distance to the edge of the observable universe is the boundary that represents the maximum distance at which events can currently be observed. For events beyond that distance, light hasn't 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 It is an intrinsic expansion—that is, it is defined by the relative separation of parts of the universe and not by motion "outward" into preexisting space.. 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 can't 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 d_E by

In this equation, a is the scale factor 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. It relates the comoving distances for an expanding universe with the distances at a reference time arbitrarily taken to be the present, c is the speed of light The speed of light, usually denoted by c, is a physical constant, so named because it is the speed at which light and all other electromagnetic radiation travels in vacuum. Its value is exactly 299,792,458 metres per second, often approximated as 300,000 kilometres per second or 186,000 miles per second. In the theory of relativity, c connects, 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 is a general term for the substance of which all physical objects are made. Typically, this includes atoms and other particles which have mass. However in practice there is no single correct scientific meaning; each field uses the term in different and often incompatible ways. A common way of defining matter is as anything that has mass and or by radiation Light is electromagnetic radiation of a wavelength that is visible to the human eye . In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not. An example of a cosmological model with an event horizon is a universe dominated by the 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. Einstein abandoned the concept after the observation of the Hubble redshift indicated that the universe might not be stationary, as he had based his theory on the idea (a De Sitter universe A de Sitter universe is a 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 correspond to dark energy).

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 cones A light cone is the path that a flash of light, emanating from a single event E and traveling in all directions, would take through spacetime. If we imagine the light confined to a two-dimensional plane, the light from the flash spreads out in a circle after the event E occurs, and if we graph the growing circle with the vertical axis of the graph from these events intersect the particle's 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 perceptually straight. 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 An apparent horizon is a surface defined in general relativity as the boundary between light rays which are directed outwards and moving outwards, and those which are directed outwards but moving inwards 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 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 images of each other and resembling two infinite bows, which asymptotically approaches 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. In some contexts, such as algebraic geometry, an asymptote is 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^{[citation needed]} (in particle accelerators A particle accelerator is a device that uses electric 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, 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 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 never intersects the observer's world line). Attempting to make an object approaching the horizon remain stationary with respect to an observer requires applying a force whose magnitude becomes 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, the horizon always appears to be a fixed distance away for a non-accelerating 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 to contact the horizon, in practice this cannot be done. If the observer is lowered very slowly, then, in the observer's frame of reference, the horizon appears to be very far away and even more rope needs to be paid out to reach the horizon. If the observer is quickly lowered by another observer, then indeed the first observer and some of the rope can touch and even cross the (second observer's) event horizon. If the rope is pulled taut to fish the first observer back out, then 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.

Attempting to stick a rigid rod through the hole's horizon cannot be done: if the rod is lowered extremely slowly, then it is always too short to touch the event horizon, as the coordinate frames near the tip of the rod are extremely compressed. From the point of view of an observer at the end of the rod, the event horizon remains hopelessly out of reach. If the rod is lowered quickly, then the same problems as with the rope are encountered: the rod must break and the broken-off pieces inevitably fall in.

These peculiarities only occur because of the supposition that the observers be stationary with respect to some other distant observer. Observers who fall into the hole are moving with respect to the distant observer and so perceive the horizon as being in a different location, seeming to recede in front of them so that they never contact it. Increasing tidal forces (and eventual impact with the hole's gravitational singularity) are the only locally noticeable effects. While this seems to allow an in-falling observer to relay information from objects outside their perceived horizon but inside the distant observer's perceived horizon, in practice the horizon recedes by an amount small enough that by the time the in-falling observer receives any signal from farther into the hole, they've already crossed what the distant observer perceived to be the horizon and this reception event (and any retransmission) can't be seen by the distant observer.

Beyond general relativity

The description of event horizons given by general relativity is thought to be incomplete. When the conditions under which event horizons occur are modelled using a more complete picture of the way the universe works, that includes both relativity and quantum mechanics, 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 and so emit radiation. For black holes, this manifests as Hawking radiation, and the larger question of how the black hole possesses a temperature is part of the topic of black hole thermodynamics. For accelerating particles, this manifests as the Unruh effect, 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. One such candidate theory is M-theory. Another such candidate theory is Loop Quantum Gravity.

See also

• Acoustic horizon
• Hawking radiation
• Cosmic censorship
• Rindler coordinates

References

• The Universe in a Nutshell by Stephen Hawking
• Kip Thorne (1994). Black Holes and Time Warps. W. W. Norton.
• Abhay Ashtekar and Badri Krishnan, “Isolated and Dynamical Horizons and Their Applications”, Living Rev. Relativity, 7, (2004), 10; Online Article, cited Feb.2009.

More technical references

1. ^ S. W. Hawking and G. F. R. Ellis (1975). The large scale structure of space-time. Cambridge University Press. ^{[page needed]}
2. ^ Thorne, Kip S.; Misner, Charles; Wheeler, John (1973). Gravitation. W. H. Freeman and Company. ^{[page needed]}
3. ^ Wald, Robert M. (1984). General Relativity. Chicago: University of Chicago Press. ^{[page needed]}
4. ^ J. A. Peacock (1999). Cosmological Physics. Cambridge University Press. ^{[page needed]}

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