1109.5274 (Fabio Grangeiro Rodrigues et al.)

Maxwell and Navier-Stokes Equations Equivalent to Einstein Equation    [PDF]

Fabio Grangeiro Rodrigues, Roldao da Rocha, Waldyr A. Rodrigues Jr

In this paper we are concerned to reveal that any spacetime structure },\uparrow>, which is a model of a gravitational field in General Relativity generated by an energy-momentum tensor T --- and which contains at least one Killing vector field A --- is such that the 2-form field F=dA (where A=[g]\slg(A,)), satisfies a Maxwell like equation --- with a well determined current that contains a term of the superconducting type. Moreover, the Maxwell equations for F are straightforwardly shown to be equivalent to Einstein equation and to Navier-Stokes equation as well. As a result, we have a set consisting of Einstein, Maxwell and Navier-Stokes equations that are completely equivalent from the mathematical point of view, once some identifications about field variables are evinced, as detailed explained throughout the text. We compare and emulate our results with others on the same subject appearing in the literature.

View original: http://arxiv.org/abs/1109.5274