In
general relativity
General relativity, also known as the general theory of relativity, and as Einstein's theory of gravity, is the differential geometry, geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of grav ...
, an absolute horizon is a boundary in
spacetime
In physics, spacetime, also called the space-time continuum, is a mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams are useful in visualiz ...
, 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 massive, compact astronomical object so dense that its gravity prevents anything from escaping, even light. Albert Einstein's theory of general relativity predicts that a sufficiently compact mass will form a black hole. Th ...
.
In the context of black holes, the absolute horizon is generally referred to as an
event horizon
In astrophysics, an event horizon is a boundary beyond which events cannot affect an outside 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 c ...
, 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 horizons; 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)
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;United States
*Kerr Township, Champaign County, Illinois
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*Kerr, Ohio, an unincorporated community
*Kerr County, Texas
Kerr Co ...
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 ray
In optics, a ray is an idealized geometrical model of light or other electromagnetic radiation, 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 ...
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 Applet ...
'', 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 mathematically convenient and does not depend on the observer, unlike
apparent horizons, for example. The disadvantage is that it requires the full history (all the way into the future) of the spacetime to be known, thus making event horizons unsuitable for empirical tests.
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 possible causal relationships between points in the manifold.
Lorentzian manifolds can be classified according to the types of causal structures they admit (''c ...
*
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 geodesi ...
*
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. ...
*
Ergosphere
file:Kerr surfaces.svg, 300px, At the ergospheres (shown here in violet for the outer and red for the inner one), the temporal metric coefficient ''gtt'' becomes negative, i.e., acts like a purely spatial metric component. Consequently, timelike or ...
*
Killing horizon
In physics, a Killing horizon is a geometrical construct used in general relativity and its generalizations to delineate spacetime boundaries without reference to the dynamic Einstein field equations. Mathematically a Killing horizon is a null hyp ...
*
Naked singularity
*
Particle horizon
The particle horizon (also called the cosmological horizon, the comoving horizon (in Scott 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 o ...
*
Photon sphere
A photon sphere, or photon ring or photon circle, arises in a neighbourhood of the event horizon of a black hole where gravity is so strong that emitted photons will not just bend around the black hole but also return to the point where they we ...
*
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 assumpti ...
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 ...
, date=1994 This is a popular book, aimed at the lay reader, containing good discussion of horizons and black holes.
Concepts in astrophysics
General relativity