Black Hole Entropy production and Transport coefficients in Lovelock Gravity

TL;DR

This paper explores black hole entropy evolution in Lovelock gravity, revealing that the analogy between horizon entropy change and fluid dynamics extends beyond general relativity, with viscosities matching membrane paradigm and holographic results.

Contribution

It introduces a thermodynamic framework for black hole entropy in Lovelock gravity and demonstrates the exact match of shear and bulk viscosities with established paradigms.

Findings

Entropy change expressions in Lovelock gravity resemble fluid dynamics.

Shear and bulk viscosities match membrane paradigm results.

Viscosities also agree with holographic calculations.

Abstract

We study the entropy evolution of black holes in Lovelock gravity by formulating a thermodynamic generalization of null Raychaudhuri equation. We show that the similarity between the expressions of entropy change of the black hole horizon due to perturbation and that of a fluid, which is out of equilibrium, transcends beyond general relativity to the Lovelock class of theories. Exploiting this analogy we find that the shear and bulk viscosities for the black holes in Lovelock theories exactly match with those obtained in the membrane paradigm and also from holographic considerations.