Smarr Formula for Lovelock Black Holes: a Lagrangian approach

TL;DR

This paper derives a generalized Smarr Formula for Lovelock black holes using a Lagrangian and Noether charge approach, incorporating topological contributions to entropy.

Contribution

It extends Wald's formalism to Lovelock gravity, providing a new volume integral expression for the Smarr Formula and a novel entropy prescription.

Findings

Derived a surface and volume integral form of the Smarr Formula for Lovelock black holes

Proposed a new entropy functional including topological terms

Applied the formalism to compute mass and entropy of static Lovelock black holes

Abstract

We argue that the Smarr Formula for black holes can be expressed in terms of a Noether charge surface integral plus a suitable volume integral, for any gravitational theory. The integrals can be constructed as an application of Wald's formalism. We apply this formalism to compute the mass and the Smarr Formula for static Lovelock black holes. Finally, we propose a new prescription for Wald's entropy in the case of Lovelock black holes, which takes into account topological contributions to the entropy functional.