We analyze the field equations of Lovelock gravity for the Kerr-Schild metric ansatz, gab = g ̄ab + λkakb, with background metric g ̄ab, 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 λ^2. More general Gauss-Bonnet theories having two distinct vacua yield a pair of equations, at orders λ and λ^2 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 λ^n with 1 ≤ n ≤ p. An examination of known static black hole solutions also supports this conclusion.
Available at: http://works.bepress.com/david_kastor/34/