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In general relativity, an event horizon is a boundary in spacetime, an area surrounding a black hole, beyond which events cannot affect an outside observer. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Light emitted from inside the horizon can never reach the observer, and anything that passes through the horizon from the observer's side is never seen again.

More specific types of horizon include the related but distinct absolute and apparent horizons found around a black hole. 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 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 Still other distinct notions include the Cauchy and Killing horizon; the photon spheres and ergospheres of the Reissner-Nordström solution; particle and cosmological horizons relevant to cosmology; and isolated and dynamical horizons important in current black hole research. In Physics, a Cauchy horizon is a Light-like boundary of the domain of validity of a Cauchy problem (a particular Boundary value problem of the A Killing horizon is a null hypersurface on which there is a null Killing vector field A photon sphere is a Spherical region of space where Gravity is strong enough that Photons of light are forced to travel in orbits The ergosphere is a region located outside a Rotating black hole. In Physics and Astronomy, the Reissner-Nordström metric is a solution to the Einstein field equations in empty space which corresponds to the gravitational In Physical cosmology, particle horizon is the maximum distance from which particles could have traveled to the observer in the Age of the universe In Physical cosmology, a cosmological horizon marks a limit to observability and marks the boundary of a region that an observer cannot see into directly Cosmology (from Greek grc κοσμολογία - grc κόσμος kosmos, "universe" and grc -λογία -logia) is study

An event horizon is generated by a family of null geodesic rays. In Mathematics, a geodesic /ˌdʒiəˈdɛsɪk -ˈdisɪk/ -dee-sik is a generalization of the notion of a " straight line " to " curved spaces

Event horizon of a black hole

Main article: Black hole

The most commonly known example of an event horizon is defined around general relativity's description of a black hole, a celestial object so dense that no matter or radiation can escape its gravitational field. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e A gravitational field is a model used within Physics to explain how gravity exists in the universe This is sometimes described as the boundary within which the black hole's escape velocity is greater than the speed of light. In Physics, escape velocity is the speed where the Kinetic energy of an object is equal to the magnitude of its Gravitational potential energy This definition only works if the effects of special and general relativity are taken into account. 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 cones of particles within the horizon, are warped so as to fall further into the hole. In Physics and Mathematics, Minkowski space (or Minkowski spacetime) is the mathematical setting in which Einstein's theory of Special relativity In Special relativity, a light cone (or null cone) is the pattern describing the temporal evolution of a flash of Light in Minkowski spacetime 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 acts as an event horizon in a non-rotating body that fits inside this radius. The Schwarzschild radius (sometimes historically referred to as the gravitational radius) is a characteristic Radius associated with every Mass. (A rotating black hole operates slightly differently. Black hole#Major features of rotating black holes A rotating black hole is a Black hole that possesses Angular momentum. ) The Schwarzschild radius of an object is proportional to the mass. For the mass of the Sun it is approximately 3 km, and for that of the Earth about 9 mm. The Sun (Sol is the Star at the center of the Solar System. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 For a black hole created by the collapse of a star (which has a mass above the Chandrasekhar limit) the lower limit is about 4 km. The Chandrasekhar limit limits the mass of bodies made from Electron-degenerate matter, a dense form of matter which consists of nuclei immersed in a gas of Electrons

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 passing 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 effects become significant near the vicinity of the event horizon. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature This allows observations of matter in the vicinity of a black hole's event horizon to be used to indirectly study general relativity and proposed extensions to it. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916

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 However, modern usage has brought those ideas under the umbrella of the term "event horizon". (See, e. g. ,^[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 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

Main article: Ultimate fate of the universe

The particle horizon of the observable universe is the boundary that represents the maximum distance at which events can currently be observed. The ultimate fate of the universe is a topic in Physical cosmology. In Physical cosmology, particle horizon is the maximum distance from which particles could have traveled to the observer in the Age of the universe In Big Bang Cosmology, the observable universe is the region of space bounded by a Sphere, centered on the observer that is small enough that 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. The metric expansion of space is the averaged increase of metric (i If the expansion has appropriate 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, c is the speed of light, and t₀ is the age of the universe. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model is a function of time which represents the relative expansion of the Universe If , points arbitrarily far away can be observed, and no event horizon exists. If , a horizon is present.

Examples of cosmological models without an event horizon are universes dominated by matter or by radiation. Matter is commonly defined as being anything that has mass and that takes up space. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 An example of a cosmological model with an event horizon is a universe dominated by the cosmological constant (a de Sitter universe). In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification A de Sitter universe is a solution to Einstein 's field equations of General Relativity which is named after Willem de Sitter.

Event horizon of an accelerated particle

Spacetime diagram showing a uniformly accelerated particle, P, and an event E that is outside the particle's event horizon. The event's forward light cone never intersects the particle's world line. In Special relativity, a light cone (or null cone) is the pattern describing the temporal evolution of a flash of Light in Minkowski spacetime In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime.

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 from these events intersect the particle's world line. In Special relativity, a light cone (or null cone) is the pattern describing the temporal evolution of a flash of Light in Minkowski spacetime In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. 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 event horizon 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 spacetime 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 spacetime diagram, its path is a hyperbola, which asymptotically approaches a 45 degree line (the path of a light ray). In Geometry, a hyperbola ( Greek, "over-thrown" has several equivalent definitions An asymptote of a real-valued function y=f(x is a curve which describes the behavior of f as either x or y goes to infinity 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 event horizon).

While approximations of this type of situation can occur in the real world (in particle accelerators, 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. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e In practice, several features are common to all event horizons: they 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). In Special relativity, a light cone (or null cone) is the pattern describing the temporal evolution of a flash of Light in Minkowski spacetime In physics the world line of an object is the unique path of that object as it travels through 4- Dimensional Spacetime. 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. A de Sitter universe is a solution to Einstein 's field equations of General Relativity which is named after Willem de Sitter. In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest 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 ever more rope needs to be paid out to reach the horizon. If the observer is lowered quickly, then indeed the observer, and some of the rope can touch and even cross the (distant lowerer's) event horizon. If the rope is pulled taut to fish the 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 lowerer 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 that 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. The tidal force is a secondary effect of the Force of Gravity and is responsible for the Tides It arises because the gravitational acceleration experienced A gravitational singularity (sometimes spacetime singularity) is approximately a place where quantities which are used to measure the Gravitational field become While this seems to allow an infalling 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 infalling 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. General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 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. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons

At present, it is expected that the primary impact of quantum effects is for event horizons to possess a temperature and so emit radiation. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature 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. A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes 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 For accelerating particles, this manifests as the Unruh effect, which causes space around the particle to appear to be filled with matter and radiation. The Unruh effect, discovered in 1976 by Bill Unruh of the University of British Columbia, is the prediction that an accelerating observer will observe

A complete description of event horizons is expected to at minimum require a theory of quantum gravity. Quantum gravity is the field of Theoretical physics attempting to unify Quantum mechanics, which describes three of the fundamental forces of nature One such candidate theory is M-theory. In Theoretical physics, M-theory is a new limit of String theory in which 11 dimensions of Spacetime may be identified

See also

• Acoustic horizon
• Hawking radiation
• Cosmic censorship

References

• The Universe in a Nutshell by Stephen Hawking
• Kip Thorne (1994). In Mathematical physics, a metric describes the arrangement of relative distances within a surface or volume usually measured by signals passing through the region – essentially Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes The weak and the strong Cosmic Censorship Hypotheses are two mathematical conjectures about the structure of singularities arising in General relativity. The Universe in a Nutshell is one of Stephen Hawking 's latest books on Theoretical physics. Stephen William Hawking CH, CBE, FRS, FRSA (born 8 January 1942 is a British theoretical physicist. Black Holes and Time Warps. W. W. Norton.  

More technical references

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