The Second Law in 4D Einstein-Gauss-Bonnet Gravity

Abstract

The topological contribution to black hole entropy of a Gauss-Bonnet term in four dimensions opens up the possibility of a violation of the second law of thermodynamics in black hole mergers. We show, however, that the second law is not violated in the regime where Einstein-Gauss-Bonnet holds as an effective theory and black holes can be treated thermodynamically. For mergers of AdS black holes, the second law appears to be violated even in Einstein gravity; we argue, however, that the second law holds when gravitational potential energy is taken into account.