Absolute horizon
Encyclopedia
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 horizon is the boundary of a black hole
by definition.
In the context of black holes, the absolute horizon is almost exclusively referred to as an event horizon
, though this is often used as a more general term for all types of horizons. The absolute horizon is just one type of horizon. For example, important distinctions must be made between absolute horizons and apparent horizon
s. See also the articles on ergosphere
, Cauchy horizon
, the Reissner-Nordström solution, photon sphere, Killing horizon
and naked singularity
; the notion of a horizon in general relativity is subtle, and depends on fine distinctions.
— a spacetime which approaches flat space as one moves far away from any massive bodies. Examples of asymptotically flat spacetimes include Schwarzschild
and Kerr
black holes. The FRW universe — which is believed to be a good model for our universe — is generally not asymptotically flat. Nonetheless, we can think of an isolated object in an FRW universe as being nearly an isolated object in an asymptotically flat universe.
The particular feature of asymptotic flatness which is needed is a notion of "future null infinity". This is the set of points which are approached asymptotically by null rays (light rays, for example) which can escape to infinity. This is the technical meaning of "external universe". These points are only defined in an asymptotically flat universe. An absolute horizon is defined as the boundary
of a region from which null rays cannot escape to future null infinity.
s, for example. The disadvantage is that it requires the full history (all the way into the future) of the spacetime to be known. In the case of numerical relativity
, where a spacetime is simply being evolved into the future, only a finite portion of the spacetime can be known.
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 absolute 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...
, 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 horizon is the boundary 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...
by definition.
In the context of black holes, the absolute horizon is almost exclusively referred to as an event horizon
Event horizon
In general relativity, an event horizon is a boundary in spacetime 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...
, though this is often used as a more general term for all types of horizons. The absolute horizon is just one type of horizon. For example, important distinctions must be made between absolute horizons 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. See also the articles on 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...
, Cauchy horizon
Cauchy horizon
In physics, a Cauchy horizon is a light-like boundary of the domain of validity of a Cauchy problem...
, the Reissner-Nordström solution, photon sphere, 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...
and naked singularity
Naked singularity
In general relativity, a naked singularity is a gravitational singularity, without an event horizon. In a black hole, there is a region around the singularity, the event horizon, where the gravitational force of the singularity is strong enough so that light cannot escape. Hence, the singularity...
; the notion of a horizon in general relativity is subtle, and depends on fine distinctions.
Definition
An absolute horizon is only defined in an asymptotically flat spacetimeAsymptotically flat spacetime
An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime....
— a spacetime which approaches flat space as one moves far away from any massive bodies. Examples of asymptotically flat spacetimes include Schwarzschild
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
and Kerr
Kerr metric
The Kerr metric describes the geometry of empty spacetime around an uncharged axially-symmetric black-hole with an event horizon which is topologically a sphere. The Kerr metric is an exact solution of the Einstein field equations of general relativity; these equations are highly non-linear, which...
black holes. The FRW universe — which is believed to be a good model for our universe — is generally not asymptotically flat. Nonetheless, we can think of an isolated object in an FRW universe as being nearly an isolated object in an asymptotically flat universe.
The particular feature of asymptotic flatness which is needed is a notion of "future null infinity". This is the set of points which are approached asymptotically by null rays (light rays, for example) which can escape to infinity. This is the technical meaning of "external universe". These points are only defined in an asymptotically flat universe. An absolute horizon is defined as the boundary
Boundary (topology)
In topology and mathematics in general, the boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S. More precisely, it is the set of points in the closure of S, not belonging to the interior of S. An element of the boundary...
of a region from which null rays cannot escape to future null infinity.
Nature of the absolute horizon
The definition of an absolute horizon is sometimes referred to as teleological, meaning that it cannot be known where the absolute horizon is without knowing the entire evolution of the universe, including the future. This is both an advantage and a disadvantage. The advantage is that this notion of a horizon is very geometrical, and does not depend on the observer, unlike apparent horizonApparent 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, for example. The disadvantage is that it requires the full history (all the way into the future) of the spacetime to be known. In the case of numerical relativity
Numerical relativity
Numerical relativity is one of the branches of general relativity that uses numerical methods and algorithms to solve and analyze problems. To this end, supercomputers are often employed to study black holes, gravitational waves, neutron stars and many other phenomena governed by Einstein's Theory...
, where a spacetime is simply being evolved into the future, only a finite portion of the spacetime can be known.
See also
- Event horizonEvent horizonIn general relativity, an event horizon is a boundary in spacetime 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...
- Apparent horizonApparent horizonIn 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...
- Black holeBlack holeA 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...
- Schwarzschild metricSchwarzschild metricIn Einstein's theory of general relativity, the Schwarzschild solution describes the gravitational field outside a spherical, uncharged, non-rotating mass such as a star, planet, or black hole. It is also a good approximation to the gravitational field of a slowly rotating body like the Earth or...
- Particle horizon
- cosmological horizon