Almost universal spacetimes in higher-order gravity theories

We study almost universal spacetimes-spacetimes for which the field equations of any generalized gravity with the Lagrangian constructed fromthe metric, the Riemann tensor and its covariant derivatives of arbitrary order reduce to one single differential equation and one algebraic condition for the Ricci scalar. We prove that all d-dimensional Kundt spacetimes ofWeyl type III and traceless Ricci type N are almost universal. Explicit examples ofWeyl type II almost universalKundt metrics are also given. The considerable simplification of the field equations of higher-order gravity theories for almost universal spacetimes is then employed to study new Weyl type II, III, and N vacuum solutions to quadratic gravity in arbitrary dimension and six-dimensional conformal gravity. Necessary conditions for almost universal metrics are also studied.