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arXiv · 0812.3194

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

Andres Anabalon·Nathalie Deruelle·Yoshiyuki Morisawa·Julio Oliva·Misao Sasaki·David Tempo·Ricardo Troncoso
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Abstract

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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Andres Anabalon, Nathalie Deruelle, Yoshiyuki Morisawa, Julio Oliva, Misao Sasaki, David Tempo, Ricardo Troncoso. 2009-01-21. Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions. https://doi.org/10.1088/0264-9381%2F26%2F6%2F065002

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