TY - JOUR

T1 - Kerr-Schild ansatz in Einstein-Gauss-Bonnet gravity

T2 - An exact vacuum solution in five dimensions

AU - Anabalón, Andrés

AU - Deruelle, Nathalie

AU - Morisawa, Yoshiyuki

AU - Oliva, Julio

AU - Sasaki, Misao

AU - Tempo, David

AU - Troncoso, Ricardo

PY - 2009

Y1 - 2009

N2 - 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 ≠ 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.

AB - 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 ≠ 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.

UR - http://www.scopus.com/inward/record.url?scp=68949163222&partnerID=8YFLogxK

U2 - 10.1088/0264-9381/26/6/065002

DO - 10.1088/0264-9381/26/6/065002

M3 - Article

AN - SCOPUS:68949163222

SN - 0264-9381

VL - 26

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 6

M1 - 065002

ER -