Evaluating the Wald Entropy from two-derivative terms in quadratic actions

Understand

We evaluate the Wald Noether charge entropy for a black hole in generalized theories of gravity.

• Expanding the Lagrangian to second order in gravitational perturbations, we show that contributions to the entropy density originate only from the coefficients of two-derivative terms.
• The same considerations are extended to include matter fields and to show that arbitrary powers of matter fields and their symmetrized covariant derivatives cannot contribute to the entropy density.
• We also explain how to use the linearized gravitational field equation rather than quadratic actions to obtain the same results.