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

A. Anabalon N. Deruelle 1 Y. Morisawa J. Oliva M. Sasaki 2 D. Tempo R. Troncoso
1 APC - THEORIE
APC (UMR_7164) - AstroParticule et Cosmologie, Institut für theoretische Physik
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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Submitted on : Tuesday, January 20, 2009 - 3:13:41 PM
Last modification on : Saturday, September 19, 2020 - 4:50:58 AM

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A. Anabalon, N. Deruelle, Y. Morisawa, J. Oliva, M. Sasaki, et al.. Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity: An exact vacuum solution in five dimensions. Classical and Quantum Gravity, IOP Publishing, 2009, 26, pp.065002. ⟨10.1088/0264-9381/26/6/065002⟩. ⟨in2p3-00354662⟩

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