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Komar Integrals in Higher (and Lower) Derivative Gravity

David Kastor

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.

Komar Integrals in Higher (and Lower) Derivative Gravity

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.

Paper Structure

This paper contains 9 sections, 50 equations.

Table of Contents

  1. Introduction
  2. Lovelock Gravity
  3. Komar integrals in pure Lovelock gravities
  4. Example: black holes in pure Lovelock gravity
  5. Lower derivative gravity: $\Lambda\ne 0$?
  6. Example: Schwarzschild-AdS
  7. Komar integrals in general Lovelock gravity
  8. Example: Gauss-Bonnet gravity
  9. Conclusions