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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 equation. [2]
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.
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):
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 ...
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]
1903 – Olinto De Pretto presents his aether theory with some form of mass–energy equivalence. [15] It was described by a formula looking like Einstein’s E = mc 2, but with different meanings of the terms. 1903 – Frederick Thomas Trouton and H.R. Noble publish the results of their experiment with capacitors, showing no aether drift. [16 ...
Albert Einstein, who had developed his theory of general relativity in 1915, initially denied the possibility of black holes, [4] even though they were a genuine implication of the Schwarzschild metric, obtained by Karl Schwarzschild in 1916, the first known non-trivial exact solution to Einstein's field equations. [1]
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. In astrophysics , fluid solutions are often employed as stellar models , since a perfect gas can be thought of as a special case of a perfect fluid.