Article Dans Une Revue Classical and Quantum Gravity Année : 2009

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

A. Anabalon
  • Fonction : Auteur
N. Deruelle
  • Fonction : Auteur
Y. Morisawa
  • Fonction : Auteur
J. Oliva
  • Fonction : Auteur
D. Tempo
  • Fonction : Auteur
R. Troncoso
  • Fonction : Auteur

Résumé

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.

Dates et versions

in2p3-00354662 , version 1 (20-01-2009)

Identifiants

Citer

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, 2009, 26, pp.065002. ⟨10.1088/0264-9381/26/6/065002⟩. ⟨in2p3-00354662⟩
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