Kerr-Schild Ansatz in Lovelock Gravity

الأصل · EN

We analyze the field equations of Lovelock gravity for the Kerr-Schild metric ansatz, gab= gab +λkₐkb, with background metric gab, background null vector kᵃ and free parameter λ. Focusing initially on the Gauss-Bonnet case, we find a simple extension of the Einstein gravity results only in theories having a unique constant curvature vacuum. The field equations then reduce to a single equation at order λ². More general Gauss-Bonnet theories having two distinct vacua yield a pair of equations, at orders λ and λ² that are not obviously compatible. Our results for higher order Lovelock theories are less complete, but lead us to expect a similar conclusion. Namely, the field equations for Kerr-Schild metrics will reduce to a single equation of order λᵖ for unique vacuum theories of order p in the curvature, while non-unique vacuum theories give rise to a set of potentially incompatible equations at orders λⁿ with 1≤ n ≤ p. An examination of known static black hole solutions also supports this conclusion.