Dynamical Black Hole Entropy in Effective Field Theory

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