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But if one requires an exact solution or a solution describing strong fields, the evolution of both the metric and the stress–energy tensor must be solved for at once. To obtain solutions, the relevant equations are the above quoted EFE (in either form) plus the continuity equation (to determine the evolution of the stress–energy tensor):
The study of exact solutions of Einstein's field equations is one of the activities of cosmology. It leads to the prediction of black holes and to different models of evolution of the universe. One can also discover new solutions of the Einstein field equations via the method of orthonormal frames as pioneered by Ellis and MacCallum. [22]
In general relativity, an exact solution is a (typically closed form) solution of the Einstein field equations whose derivation does not invoke simplifying approximations of the equations, though the starting point for that derivation may be an idealized case like a perfectly spherical shape of matter.
Einstein's theory of general relativity (including the cosmological constant) is thought to be the only theory of gravity that satisfies the strong equivalence principle. A number of alternative theories, such as Brans–Dicke theory and the Einstein-aether theory add additional fields.
Mass–energy equivalence states that all objects having mass, or massive objects, have a corresponding intrinsic energy, even when they are stationary.In the rest frame of an object, where by definition it is motionless and so has no momentum, the mass and energy are equal or they differ only by a constant factor, the speed of light squared (c 2).
The two-postulate basis for special relativity is the one historically used by Einstein, and it is sometimes the starting point today. As Einstein himself later acknowledged, the derivation of the Lorentz transformation tacitly makes use of some additional assumptions, including spatial homogeneity, isotropy, and memorylessness. [3]
These generally covariant theories describes a spacetime endowed with both a metric and a unit timelike vector field named the aether. The aether in this theory is "a Lorentz-violating vector field" [1] unrelated to older luminiferous aether theories; the "Einstein" in the theory's name comes from its use of Einstein's general relativity ...
where (,) and (,) are two metric potentials dependent on Weyl's canonical coordinates {,}.The coordinate system {,,,} serves best for symmetries of Weyl's spacetime (with two Killing vector fields being = and =) and often acts like cylindrical coordinates, [2] but is incomplete when describing a black hole as {,} only cover the horizon and its exteriors.