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The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution, found in 1949 by Kurt Gödel, [1] of the Einstein field equations in which the stress–energy tensor contains two terms: the first representing the matter density of a homogeneous distribution of swirling dust particles (see dust solution), and the second associated with a negative cosmological ...
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.
The results of various experiments, including the Michelson–Morley experiment in 1887 (subsequently verified with more accurate and innovative experiments), led to the theory of special relativity, by showing that the aether did not exist. [20] Einstein's solution was to discard the notion of an aether and the absolute state of rest.
In general relativity, a lambdavacuum solution is an exact solution to the Einstein field equation in which the only term in the stress–energy tensor is a cosmological constant term. This can be interpreted physically as a kind of classical approximation to a nonzero vacuum energy .
This contradicts the mass–energy equivalence formula, which requires the relation = / without the 4 ⁄ 3 factor, or in other words, four-momentum doesn't properly transform like a four-vector when the 4 ⁄ 3 factor is present. Laue found a solution equivalent to Poincaré's introduction of a non-electromagnetic potential (Poincaré stresses ...
p. 40: "The cradle of special theory of relativity was the combination of Maxwellian electromagnetism and the electron theory of Lorentz (and to a lesser extent of Larmor) based on Fresnel's notion of the stationary aether…. It is well known that Einstein's special relativity was partially motivated by this failure [to find the aether wind ...
[p 6] Over the next several decades, the understanding of energy and its relationship with momentum were further developed by Einstein and other physicists including Max Planck, Gilbert N. Lewis, Richard C. Tolman, Max von Laue (who in 1911 gave a comprehensive proof of M 0 = E 0 /c 2 from the stress–energy tensor [19]), and Paul Dirac (whose ...
In mathematics, and in particular gauge theory and complex geometry, a Hermitian Yang–Mills connection (or Hermite–Einstein connection) is a Chern connection associated to an inner product on a holomorphic vector bundle over a Kähler manifold that satisfies an analogue of Einstein's equations: namely, the contraction of the curvature 2-form of the connection with the Kähler form is ...