# Category: Exact solutions in general relativity

Milne model
The Milne model was a special-relativistic cosmological model proposed by Edward Arthur Milne in 1935. It is mathematically equivalent to a special case of the FLRW model in the limit of zero energy d
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 fi
Anti-de Sitter space
In mathematics and physics, n-dimensional anti-de Sitter space (AdSn) is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. Anti-de Sitter space and de Sitter space are
Static universe
In cosmology, a static universe (also referred to as stationary, infinite, static infinite or static eternal) is a cosmological model in which the universe is both spatially and temporally infinite, a
Fluid solution
In general relativity, a fluid solution is an exact solution of the Einstein field equation in which the gravitational field is produced entirely by the mass, momentum, and stress density of a fluid.
Pp-wave spacetime
In general relativity, the pp-wave spacetimes, or pp-waves for short, are an important family of exact solutions of Einstein's field equation. The term pp stands for plane-fronted waves with parallel
Vaidya metric
In general relativity, the Vaidya metric describes the non-empty external spacetime of a spherically symmetric and nonrotating star which is either emitting or absorbing null dusts. It is named after
McVittie metric
In the general theory of relativity, the McVittie metric is the exact solution of Einstein's field equations describing a black hole or massive object immersed in an expanding cosmological spacetime.
Derivation of the Schwarzschild solution
The Schwarzschild solution describes spacetime under the influence of a massive, non-rotating, spherically symmetric object. It is considered by some to be one of the simplest and most useful solution
Van Stockum dust
In general relativity, the van Stockum dust is an exact solution of the Einstein field equation in which the gravitational field is generated by dust rotating about an axis of cylindrical symmetry. Si
Weyl metrics
In general relativity, the Weyl metrics (named after the German-American mathematician Hermann Weyl) are a class of static and axisymmetric solutions to Einstein's field equation. Three members in the
Distorted Schwarzschild metric
In physics, the distorted Schwarzschild metric is the metric of a standard/isolated Schwarzschild spacetime exposed in external fields. In numerical simulation, the Schwarzschild metric can be distort
Ellis wormhole
The Ellis wormhole is the special case of the Ellis drainhole in which the 'ether' is not flowing and there is no gravity. What remains is a pure traversable wormhole comprising a pair of identical tw
Ozsváth–Schücking metric
The Ozsváth–Schücking metric, or the Ozsváth–Schücking solution, is a vacuum solution of the Einstein field equations. The metric was published by István Ozsváth and Engelbert Schücking in 1962. It is
Exact solutions in general relativity
In general relativity, an exact solution is a solution of the Einstein field equations whose derivation does not invoke simplifying assumptions, though the starting point for that derivation may be an
BKL singularity
A Belinski–Khalatnikov–Lifshitz (BKL) singularity is a model of the dynamic evolution of the universe near the initial gravitational singularity, described by an anisotropic, chaotic solution of the E
Relativistic disk
In general relativity, the relativistic disk expression refers to a class of axi-symmetric self-consistent solutions to Einstein's field equations corresponding to the gravitational field generated by
Monochromatic electromagnetic plane wave
In general relativity, the monochromatic electromagnetic plane wave spacetime is the analog of the monochromatic plane waves known from Maxwell's theory. The precise definition of the solution is quit
Tolman–Oppenheimer–Volkoff equation
In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modelled
De Sitter space
In mathematical physics, n-dimensional de Sitter space (often abbreviated to dSn) is a maximally symmetric Lorentzian manifold with constant positive scalar curvature. It is the Lorentzian analogue of
Schwarzschild geodesics
In general relativity, Schwarzschild geodesics describe the motion of test particles in the gravitational field of a central fixed mass that is, motion in the Schwarzschild metric. Schwarzschild geode
Lemaître–Tolman metric
In mathematical physics, the Lemaître–Tolman metric is the spherically symmetric dust solution of Einstein's field equations. It was first found by Georges Lemaître in 1933 and Richard Tolman in 1934
Minkowski space
In mathematical physics, Minkowski space (or Minkowski spacetime) (/mɪŋˈkɔːfski, -ˈkɒf-/) is a combination of three-dimensional Euclidean space and time into a four-dimensional manifold where the spac
Friedmann–Lemaître–Robertson–Walker metric
The Friedmann–Lemaître–Robertson–Walker (FLRW; /ˈfriːdmən ləˈmɛtrə ... /) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous
Gravitational plane wave
In general relativity, a gravitational plane wave is a special class of a vacuum pp-wave spacetime, and may be defined in terms of Brinkmann coordinates by Here, can be any smooth functions; they cont
Null dust solution
In mathematical physics, a null dust solution (sometimes called a null fluid) is a Lorentzian manifold in which the Einstein tensor is null. Such a spacetime can be interpreted as an exact solution of
Scalar field solution
In general relativity, a scalar field solution is an exact solution of the Einstein field equation in which the gravitational field is due entirely to the field energy and momentum of a scalar field.
Aichelburg–Sexl ultraboost
In general relativity, the Aichelburg–Sexl ultraboost is an exact solution which models the spacetime of an observer moving towards or away from a spherically symmetric gravitating object at nearly th
Belinski–Zakharov transform
The Belinski–Zakharov (inverse) transform is a nonlinear transformation that generates new exact solutions of the vacuum Einstein's field equation. It was developed by Vladimir Belinski and Vladimir Z
Dust solution
In general relativity, a dust solution is a fluid solution, a type of exact solution of the Einstein field equation, in which the gravitational field is produced entirely by the mass, momentum, and st
Kasner metric
The Kasner metric (developed by and named for the American mathematician Edward Kasner in 1921) is an exact solution to Albert Einstein's theory of general relativity. It describes an anisotropic univ
Mixmaster universe
The Mixmaster universe (named after Sunbeam Mixmaster, a brand of Sunbeam Products electric kitchen mixer) is a solution to Einstein field equations of general relativity studied by Charles Misner in
Vacuum solution (general relativity)
In general relativity, a vacuum solution is a Lorentzian manifold whose Einstein tensor vanishes identically. According to the Einstein field equation, this means that the stress–energy tensor also va
Kerr–Newman metric
The Kerr–Newman metric is the most general asymptotically flat, stationary solution of the Einstein–Maxwell equations in general relativity that describes the spacetime geometry in the region surround
Lambdavacuum solution
In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term. This can be inter
Electrovacuum solution
In general relativity, an electrovacuum solution (electrovacuum) is an exact solution of the Einstein field equation in which the only nongravitational mass–energy present is the field energy of an el
Bonnor beam
In general relativity, the Bonnor beam is an exact solution which models an infinitely long, straight beam of light. It is an explicit example of a pp-wave spacetime. It is named after William B. Bonn
Alcubierre drive
The Alcubierre drive ([alˈkubie:re]) is a speculative warp drive idea according to which a spacecraft could achieve apparent faster-than-light travel by contracting space in front of it and expanding
De Sitter universe
A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matt
Static spherically symmetric perfect fluid
In , particularly general relativity, a static spherically symmetric perfect fluid solution (a term which is often abbreviated as ssspf) is a spacetime equipped with suitable tensor fields which model
De Sitter–Schwarzschild metric
In general relativity, the de Sitter–Schwarzschild solution describes a black hole in a causal patch of de Sitter space. Unlike a flat-space black hole, there is a largest possible de Sitter black hol
Taub–NUT space
The Taub–NUT metric (/tɔːb nʌt/, /- ˌɛn.juːˈtiː/) is an exact solution to Einstein's equations. It may be considered a first attempt in finding the metric of a spinning black hole. It is sometimes als
Lemaître coordinates
Lemaître coordinates are a particular set of coordinates for the Schwarzschild metric—a spherically symmetric solution to the Einstein field equations in vacuum—introduced by Georges Lemaître in 1932.
Interior Schwarzschild metric
In Einstein's theory of general relativity, the interior Schwarzschild metric (also interior Schwarzschild solution or Schwarzschild fluid solution) is an exact solution for the gravitational field in
In theoretical physics, an anti-de Sitter (AdS) black hole is a black hole solution of general relativity or its extensions which represents an isolated massive object, but with a negative cosmologica
Gödel metric
The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution of the Einstein field equations in which the stress–energy tensor contains two terms, the first representing
Reissner–Nordström metric
In physics and astronomy, the Reissner–Nordström metric is a static solution to the Einstein–Maxwell field equations, which corresponds to the gravitational field of a charged, non-rotating, spherical
Ellis drainhole
The Ellis drainhole is the earliest-known complete mathematical model of a traversable wormhole. It is a static, spherically symmetric solution of the Einstein vacuum field equations augmented by incl
Newman–Janis algorithm
In general relativity, the Newman–Janis algorithm (NJA) is a complexification technique for finding exact solutions to the Einstein field equations. In 1964, Newman and Janis showed that the Kerr metr
Petrov classification
In differential geometry and theoretical physics, the Petrov classification (also known as Petrov–Pirani–Penrose classification) describes the possible algebraic symmetries of the Weyl tensor at each
Two-body problem in general relativity
The two-body problem in general relativity is the determination of the motion and gravitational field of two bodies as described by the field equations of general relativity. Solving the Kepler proble
Kerr metric
The Kerr metric or Kerr geometry describes the geometry of empty spacetime around a rotating uncharged axially symmetric black hole with a quasispherical event horizon. The Kerr metric is an exact sol