  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 around
maximally symmetric Einstein vacua. It is also shown that the entropy for
spherically symmetric black holes in f(Ricci) gravity calculated via Wald's
method and the boundary Noether charge approach proposed by Majhi and
Padmanabhan are in good agreement.
