The holographic entropy increases in quadratic curvature gravity

TL;DR

This paper resolves ambiguities in calculating black hole entropy in quadratic curvature gravity, demonstrating that holographic entropy increases over time, consistent with the Second Law, through explicit calculations.

Contribution

It provides a unique, physically motivated method to determine entropy in quadratic curvature gravity, aligning with holographic entanglement entropy results.

Findings

Holographic entropy increases in quadratic curvature gravity.

The entropy obeys a Second Law in Vaidya-like solutions.

The method resolves previous ambiguities in non-stationary horizons.

Abstract

Standard methods for calculating the black hole entropy beyond general relativity are ambiguous when the horizon is non stationary. We fix these ambiguities in all quadratic curvature gravity theories, by demanding that the entropy be increasing at every time, for linear perturbations to a stationary black hole. Our result matches with the entropy formula found previously in holographic entanglement entropy calculations. We explicitly calculate the entropy increase for Vaidya-like solutions in Ricci-tensor gravity to show that (unlike the Wald entropy) the holographic entropy obeys a Second Law.