Gravitational Chern-Simons Lagrangians and black hole entropy

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action. Extending previous works, w e define a general procedure, valid in any dimensions both for purely gravitational CS terms and for mixed gauge- gravitational ones. The final formula is very similar to Wald’s original formula valid for covariant actions, with a significant modification. Notwith standing an apparent violation of covariance we argue that the entropy formula is indeed covariant