Dynamical Black Hole Entropy in Effective Field Theory

TL;DR

This paper derives an explicit form of dynamical black hole entropy in 4D vacuum gravity EFTs with up to 6 derivatives, confirming gauge invariance at this order and exploring its breakdown at 8 derivatives.

Contribution

It provides the explicit form of dynamical black hole entropy for 4D vacuum gravity EFTs with up to 6 derivatives and analyzes gauge invariance issues at higher derivatives.

Findings

Entropy formula valid for up to 6 derivatives

Gauge invariance holds up to 6 derivatives

Gauge invariance can fail at 8 derivatives

Abstract

In recent work, Hollands, Kov\'acs 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.