The extended Kerr-Schild approach to general relativity
Xun Wang, Jianwei Mei
TL;DR
This paper explores an extended Kerr-Schild formulation of general relativity, decomposing metrics into functions and background tetrads, and reformulating Einstein's equations to better understand their properties.
Contribution
It introduces a novel extended Kerr-Schild approach that generalizes previous formulations and provides new insights into the structure of Einstein's equations.
Findings
Reformulation of Einstein's equations in extended Kerr-Schild form
Analysis of properties of the extended Kerr-Schild metrics
Illustrative examples demonstrating the approach
Abstract
We study in some detail the "extended Kerr-Schild" formulation of general relativity, which decomposes the gauge-independent degrees of freedom of a generic metric into two arbitrary functions and the choice of a flat background tetrad. We recast Einstein's equations and spacetime curvatures in the extended Kerr-Schild form and discuss their properties, illustrated with simple examples.
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Taxonomy
TopicsRelativity and Gravitational Theory · Algebraic and Geometric Analysis