Perturbative modes and black hole entropy in f(Ricci) gravity

f(Ricci) gravity is a special kind of higher curvature gravity whose bulk Lagrangian density is the trace of a matrix-valued function of the Ricci tensor. It is shown that under some mild constraints, f(Ricci) gravity admits Einstein manifolds as exact vacuum solutions, and can be ghost-free and tachyon-free around maximally symmetric Einstein vacua. It is also shown that the entropy for spherically symmetric black holes in f(Ricci) gravity calculated via the Wald method and the boundary Noether charge approach are in good agreement.