Entropy in Born-Infeld Gravity

TL;DR

This paper investigates entropy in Born-Infeld gravity theories, demonstrating that the macroscopic entropy aligns with the Bekenstein-Hawking entropy using an effective gravitational constant, and explores how higher curvature terms influence entropy across various dimensions.

Contribution

It establishes the equivalence of Wald and Bekenstein-Hawking entropy in Born-Infeld gravity and analyzes the impact of higher curvature terms on black hole entropy in multiple dimensions.

Findings

Wald entropy matches Bekenstein-Hawking entropy with an effective gravitational constant.

Higher curvature terms increase the entropy.

Results are extended to generic dimensions including 3, 4, and infinity.

Abstract

There is a class of higher derivative gravity theories that are in some sense natural extensions of cosmological Einstein's gravity with a unique maximally symmetric classical vacuum and only a massless spin-2 excitation about the vacuum and no other perturbative modes. These theories are of the Born-Infeld determinantal form. We show that the macroscopic dynamical entropy as defined by Wald for bifurcate Killing horizons in these theories are equivalent to the geometric Bekenstein-Hawking entropy (or more properly Gibbons-Hawking entropy for the case of de Sitter spacetime) but given with an effective gravitational constant which encodes all the information about the background spacetime and the underlying theory. We also show that the higher curvature terms increase the entropy. We carry out the computations in generic n-dimensions including the particularly interesting limits of three, four and infinite number of dimensions. We also give a preliminary discussion about the black hole entropy in generic dimensions for the BI theories.