Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions

Details Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions

2008-12-17

arxiv.org/abs/0812.3194v2

Class.Quant.Grav.26:065002,2009

Physics

High Energy Physics

High Energy Physics - Theory

10 pages, no figures, references added. Last version for CQG

Scientific paper

10.1088/0264-9381/26/6/065002

As is well-known, Kerr-Schild metrics linearize the Einstein tensor. We shall see here that they also simplify the Gauss-Bonnet tensor, which turns out to be only quadratic in the arbitrary Kerr-Schild function f when the seed metric is maximally symmetric. This property allows us to give a simple analytical expression for its trace, when the seed metric is a five dimensional maximally symmetric spacetime in spheroidal coordinates with arbitrary parameters a and b. We also write in a (fairly) simple form the full Einstein-Gauss-Bonnet tensor (with a cosmological term) when the seed metric is flat and the oblateness parameters are equal, a=b. Armed with these results we give in a compact form the solution of the trace of the Einstein-Gauss-Bonnet field equations with a cosmological term and a different than b. We then examine whether this solution for the trace does solve the remaining field equations. We find that it does not in general, unless the Gauss-Bonnet coupling is such that the field equations have a unique maximally symmetric solution.

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