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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.
In physics the Einstein-aether theory, also called aetheory, is the name coined in 2004 for a modification of general relativity that has a preferred reference frame and hence violates Lorentz invariance. These generally covariant theories describes a spacetime endowed with both a metric and a unit timelike vector field named the aether.
1. First postulate (principle of relativity) The laws of physics take the same form in all inertial frames of reference.. 2. Second postulate (invariance of c) . As measured in any inertial frame of reference, light is always propagated in empty space with a definite velocity c that is independent of the state of motion of the emitting body.
As historians such as John Stachel argue, Einstein's views on the "new aether" are not in conflict with his abandonment of the aether in 1905. As Einstein himself pointed out, no "substance" and no state of motion can be attributed to that new aether. [10] Einstein's use of the word "aether" found little support in the scientific community, and ...
Einstein's paper includes a fundamental description of the kinematics of the rigid body, and it did not require an absolutely stationary space, such as the aether. Einstein identified two fundamental principles, the principle of relativity and the principle of the constancy of light (light principle), which served as the axiomatic basis of his ...
This derivation was completely based on light speed invariance and the relativity principle, so Einstein noted that for the electrodynamics of moving bodies the aether is superfluous. Thus, the separation into "true" and "local" times of Lorentz and Poincaré vanishes – all times are equally valid and therefore the relativity of length and ...
Numerical relativity is the sub-field of general relativity which seeks to solve Einstein's equations through the use of numerical methods. Finite difference, finite element and pseudo-spectral methods are used to approximate the solution to the partial differential equations which arise. Novel techniques developed by numerical relativity ...
(Note that this does not apply in non-inertial frames, indeed between accelerating frames the speed of light cannot be constant. [1] Although it can be applied in non-inertial frames if an observer is confined to making local measurements. [2]) Einstein developed the theory of special relativity based on these two postulates.