Kerr-Schild ansatz in Lovelock gravity

The Kerr-Schild ansatz in Einstein gravity leads to a drastic simplification of the vacuum field equations. We show that in Gauss-Bonnet gravity a similar simplification occurs only in the limiting, special case that a single constant curvature vacuum state exists. In D = 5 this coincides with the theory that can be realized, in analogy with Einstein gravity in D = 3, as a Chern-Simons gauge theory. 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 simplify most drastically in theories having a unique, degenerate constant curvature vacuum.