In
general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, an absolute horizon is a boundary in
spacetime
In physics, spacetime is a mathematical model that combines the three dimensions of space and one dimension of time into a single four-dimensional manifold. Spacetime diagrams can be used to visualize relativistic effects, such as why differ ...
, defined with respect to the external universe, inside 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 by the observer. An absolute horizon is thought of as the boundary of a
black hole
A black hole is a region of spacetime where gravity is so strong that nothing, including light or other electromagnetic waves, has enough energy to escape it. The theory of general relativity predicts that a sufficiently compact mass can def ...
.
In the context of black holes, the absolute horizon is almost exclusively referred to as an
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.
In 1784, John Michell proposed that gravity can be strong enough in the vicinity of massive compact ob ...
, 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
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 outward but moving inward.
Apparent horizons are not invariant properties of spacetim ...
s; 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 spacetime – a spacetime which approaches flat space as one moves far away from any massive bodies. Examples of asymptotically flat spacetimes include
Schwarzschild and
Kerr
Kerr may refer to:
People
*Kerr (surname)
*Kerr (given name) Places
;United States
*Kerr Township, Champaign County, Illinois
*Kerr, Montana, A US census-designated place
*Kerr, Ohio, an unincorporated community
*Kerr County, Texas
Other uses
...
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
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.
Introduction
In modern physics (especially general relativity) spacetime is represented by a Lorentzian m ...
". This is the set of points which are approached asymptotically by
null rays (
light ray
In optics a ray is an idealized geometrical model of light, obtained by choosing a curve that is perpendicular to the ''wavefronts'' of the actual light, and that points in the direction of energy flow. Rays are used to model the propagation o ...
s, 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
past null cone of future null infinity.
Nature of the absolute horizon
The definition of an absolute horizon is sometimes referred to as ''
teleological
Teleology (from and )Partridge, Eric. 1977''Origins: A Short Etymological Dictionary of Modern English'' London: Routledge, p. 4187. or finalityDubray, Charles. 2020 912Teleology" In ''The Catholic Encyclopedia'' 14. New York: Robert Appleton ...
'', 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 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 outward but moving inward.
Apparent horizons are not invariant properties of spacetim ...
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 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 a ...
, where a spacetime is simply being evolved into the future, only a finite portion of the spacetime can be known.
See also
*
Causal structure
In mathematical physics, the causal structure of a Lorentzian manifold describes the causal relationships between points in the manifold.
Introduction
In modern physics (especially general relativity) spacetime is represented by a Lorentzian ma ...
*
Cauchy horizon
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 theory of partial differential equations). One side of the horizon contains closed space-like geodes ...
*
Cosmological horizon
A cosmological horizon is a measure of the distance from which one could possibly retrieve information. This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Co ...
*
Ergosphere
file:Ergosphere_and_event_horizon_of_a_rotating_black_hole_(no_animation).gif, 300px, In the ergosphere (shown here in light gray), the component ''gtt'' is negative, i.e., acts like a purely spatial metric component. Consequently, timelike or ligh ...
*
Killing horizon
*
Naked singularity
In general relativity, a naked singularity is a hypothetical gravitational singularity without an event horizon. In a black hole, the singularity is completely enclosed by a boundary known as the event horizon, inside which the curvature of s ...
*
Particle horizon The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from particles could have traveled to the observer in the age of the univer ...
*
Photon sphere
*
Reissner–Nordström solution
*
Schwarzschild metric
In Einstein's theory of general relativity, the Schwarzschild metric (also known as the Schwarzschild solution) is an
exact solution to the Einstein field equations that describes the gravitational field outside a spherical mass, on the assump ...
References
Further reading
*{{cite book , title=Black Holes and Time Warps , url=https://archive.org/details/blackholestimewa0000thor , url-access=registration , author=Kip Thorne , publisher=
W. W. Norton
W. W. Norton & Company is an American publishing company based in New York City. Established in 1923, it has been owned wholly by its employees since the early 1960s. The company is known for its Norton Anthologies (particularly ''The Norton A ...
, date=1994 This is a popular book, aimed at the lay reader, containing good discussion of horizons and black holes.
Astrophysics
General relativity