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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.
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 electromagnetic field, which must satisfy the (curved-spacetime) source-free Maxwell equations appropriate to the given geometry.
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):
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.
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 ...
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.
Kasner metric (An anisotropic solution, used to study gravitational chaos in three or more dimensions). These all belong to one or more general families of solutions: the Weyl vacua (Hermann Weyl) (the family of all static vacuum solutions), the Beck vacua (Guido Beck 1925 [2]) (the family of all cylindrically symmetric nonrotating vacuum ...
ISBN 0-470-27054-3. See chapter 6 for a more detailed exposition of white dwarf and neutron star models than can be found in other gtr textbooks. Lake, Kayll (1998). "Physical Acceptability of Isolated, Static, Spherically Symmetric, Perfect Fluid Solutions of Einstein's Equations". Comput. Phys. Commun. 115 (2–3): 395–415. arXiv: gr-qc ...