Gravitational Chern-Simons Lagrangians and black hole entropy

Understand

We analyze the problem of defining the black hole entropy when Chern-Simons terms are present in the action.

• Extending previous works, we define a general procedure, valid in any odd 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.
• Notwithstanding an apparent violation of covariance we argue that the entropy formula is indeed covariant.