Dynamical Black Hole Entropy in Effective Field Theory

In recent work, Hollands, Kovacs and Reall have built on previous work of Wall to provide a definition of dynamical black hole entropy for gravitational effective field theories (EFTs). This entropy satisfies a second law of black hole mechanics to quadratic order in perturbations around a stationary black hole. We determine the explicit form of this entropy for the EFT of 4d vacuum gravity including terms in the action with up to 6 derivatives. An open question concerns the gauge invariance of this definition of black hole entropy. We show that gauge invariance holds for the EFT of vacuum gravity with up to 6 derivatives but demonstrate that it can fail when 8 derivative terms are included. We determine an entropy for Einstein-Gauss-Bonnet theory by treating it as an EFT with vanishing 6 derivative terms.

Automated summary

Hollands, Kovacs, and Reall have defined dynamical black hole entropy for gravitational effective field theories (EFTs) building upon previous work by Wall. This entropy satisfies the second law of black hole mechanics to quadratic order in perturbations around a stationary black hole. We have determined the explicit form of this entropy for the EFT of 4d vacuum gravity, including terms in the action with up to 6 derivatives. An open question remains regarding the gauge invariance of this black hole entropy definition, which we have shown to hold for the EFT of vacuum gravity with up to 6 derivatives but can fail when 8 derivative terms are included. We have also derived an entropy for Einstein-Gauss-Bonnet theory by treating it as an EFT with vanishing 6 derivative terms.