Komar Integrals in Higher (and Lower) Derivative Gravity

TL;DR

This paper generalizes the Komar integral to Lovelock and higher derivative gravities, providing new boundary expressions for mass in AdS black holes and explicit calculations across various theories.

Contribution

It introduces a new boundary integral for Komar mass in Einstein gravity with a cosmological constant and extends the formalism to Lovelock and Gauss-Bonnet theories.

Findings

Derived a finite Komar mass for asymptotically AdS black holes.

Computed Komar masses explicitly for Lovelock and Gauss-Bonnet black holes.

Established a generalized Komar integral framework for higher derivative gravities.

Abstract

The Komar integral relation of Einstein gravity is generalized to Lovelock theories of gravity. This includes, in particular, a new boundary integral for the Komar mass in Einstein gravity with a nonzero cosmological constant, which has a finite result for asymptotically AdS black holes, without the need for an infinite background subtraction. Explicit computations of the Komar mass are given for black holes in pure Lovelock gravities of all orders and in general Gauss-Bonnet theories.