Solutions of the Einstein field equations information
Solutions of the Einstein field equations are metrics of spacetimes that result from solving the Einstein field equations (EFE) of general relativity. Solving the field equations gives a Lorentz manifold. Solutions are broadly classed as exact or non-exact.
The Einstein field equations are
where is the Einstein tensor, is the cosmological constant (sometimes taken to be zero for simplicity), is the metric tensor, is a constant, and is the stress–energy tensor.
The Einstein field equations relate the Einstein tensor to the stress–energy tensor, which represents the distribution of energy, momentum and stress in the spacetime manifold. The Einstein tensor is built up from the metric tensor and its partial derivatives; thus, given the stress–energy tensor, the Einstein field equations are a system of ten partial differential equations in which the metric tensor can be solved for.
Where appropriate, this article will use the abstract index notation.
and 19 Related for: Solutions of the Einstein field equations information
relativity. Solving thefieldequations gives a Lorentz manifold. Solutions are broadly classed as exact or non-exact. TheEinsteinfieldequations are G μ ν +...
In the general theory of relativity, theEinsteinfieldequations (EFE; also known as Einstein'sequations) relate the geometry of spacetime to the distribution...
relativity, an exact solution is a solutionoftheEinsteinfieldequations whose derivation does not invoke simplifying assumptions, though the starting point...
metric is the most general spherically symmetric vacuum solutionoftheEinsteinfieldequations. A Schwarzschild black hole or static black hole is a black...
quasispherical event horizon. The Kerr metric is an exact solutionoftheEinsteinfieldequationsof general relativity; these equations are highly non-linear...
discovered the Kerr geometry, an exact solution to theEinsteinfieldequationof general relativity. His solution models the gravitational field outside...
g_{\mu \nu }} is the spacetime metric tensor that represents thesolutionsoftheequation. Although succinct when written out using Einstein notation, hidden...
disparate points in spacetime, and is based on a special solutionoftheEinsteinfieldequations. A wormhole can be visualized as a tunnel with two ends...
holes. In addition to a black hole region in the future, such a solutionoftheEinsteinfieldequations has a white hole region in its past. This region...
first derived by Alexander Friedmann in 1922 from Einstein'sfieldequationsof gravitation for the Friedmann–Lemaître–Robertson–Walker metric and a perfect...
electrovacuum solution (electrovacuum) is an exact solutionoftheEinsteinfieldequation in which the only nongravitational mass–energy present is thefield energy...
by theEinsteinfieldequations themselves, not by a new law. Accordingly, Einstein proposed that thefieldequations would determine the path of a singular...
Schwarzschild provided the first exact solution to theEinsteinfieldequationsof general relativity, for the limited case of a single spherical non-rotating...
occurs in theEinsteinfieldequations for gravitation that describe spacetime curvature in a manner that is consistent with conservation of energy and...
Usually, fieldequations are postulated (like theEinsteinfieldequations and the Schrödinger equation, which underlies all quantum fieldequations) or obtained...
In general relativity, the van Stockum dust is an exact solutionoftheEinsteinfieldequations in which the gravitational field is generated by dust rotating...
to the Wheeler–DeWitt equation. There are relatively few known exact solutions to theEinsteinfieldequations. In order to find other solutions, there...
approximations of spacetimes that are solutions to theEinsteinfieldequation. The calculus was introduced by the Italian theoretician Tullio Regge in 1961. The starting...
Global Information
