文档介绍：The Maxwell and Navier-Stokes Equations that Follow from Einstein Equation in a
Spacetime Containing a Killing Vector Field
Fabio Grangeiro Rodrigues∗
Institute of Mathematics Statistics and putation,
-UNICAMP, 13083-950 Campinas, SP, Brazil
Waldyr A. Rodrigues Jr.†
Institute of Mathematics Statistics and putation,
-UNICAMP, 13083-950 Campinas, SP Brazil
Roldão da Rocha‡
Centro de Matemática, Computação e Cognição,
Universidade Federal do ABC, 09210-170, Santo André, SP, Brazil
(Dated: March 10 2012)
In this paper we are concerned to reveal that any spacetime structure M, g, D, g , , which is
a model of a gravitational field in General Relativity generated by an energy-momentumh ↑i tensor T
– and which contains at least one nontrivial Killing vector field A – is such that the 2-form field
F = dA (where A = g(A, )) satisfies a Maxwell like equation – with a well determined current
that contains a term of the superconducting type– which follows directly from Einstein equation.
Moreover, we show that the resulting Maxwell like equations, under an additional condition imposed
to the Killing vector field, may be written as a Navier-Stokes like equation as well. As a result,
we have a set consisting of Einstein, Maxwell and Navier-Stokes equations that follows sequentially
from the first one under precise mathematical conditions and once some identi