Noether charge and black hole entropy in modified theories of gravity

The entropy of black holes in modified theories of gravity is examined in the Palatini formalism using the Noether charge approach. It is shown that, if the gravitational coupling constant is properly identified, the entropy of a black hole is one-quarter of the horizon area in f (R) theories coupled to conformally invariant matter. If matter is present that is not conformally invariant, the entropy is still proportional to the area of the black hole, but the coefficient is generally not one-quarter. The entropy of black holes in generalized dilaton theories and in theories with Lagrangians that depend on an arbitrary function of the Ricci tensor are also examined.