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General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Phenomenology, hep-ph
Abstract:
We show how to exploit symmetry assumptions to determine the dynamical
equations for the particular geometry that underpins given matter field
equations. The procedure builds on the gravitational closure equations for
matter models without any a priori assumption of symmetry. It suffices to
illustrate the symmetrization procedure for a Klein-Gordon field equation on a
Lorentzian background, for which one obtains the Friedmann equations, without
ever having known Einstein's equations, by careful imposition of maximal
cosmological symmetry directly on the pertinent gravitational closure
equations. This method of finding the family of symmetry-reduced gravitational
field equations that are compatible with given matter dynamics directly
generalizes to any Killing symmetry algebra, matter models beyond the standard
model and indeed tensorial spacetime geometries beyond Lorentzian metrics.
