Einstein-Gauss-Bonnet theory of gravity: The Gauss-Bonnet-Katz boundary term

TL;DR

This paper introduces a new boundary term for Einstein-Gauss-Bonnet gravity, generalizing the Katz boundary term, which simplifies the calculation of black hole mass without extra regularization.

Contribution

It proposes a boundary term derived from the Chern-Weil theorem for Einstein-Gauss-Bonnet gravity, unifying various boundary conditions and reproducing known results like black hole mass.

Findings

The boundary term generalizes the Katz boundary term to Einstein-Gauss-Bonnet gravity.

It reproduces the Boulware-Deser black hole mass without additional regularization.

Includes the Gibbons-Hawking-Myers boundary as a special case.

Abstract

We propose a boundary term to the Einstein-Gauss-Bonnet action for gravity, which is constructed as the dimensional continuation of the Chern-Weil theorem, and such that the extremization of the full action yields the equations of motion when Dirichlet boundary conditions are imposed. When translated into tensorial language, this boundary term is the generalization to this theory of the Katz boundary term and vector for general relativity. The construction allows to deal with a general background and includes the Gibbons-Hawking-Myers boundary term as a special case, when the background is taken to be a product manifold. As a first application we show that this Einstein Gauss-Bonnet Katz action yields, without any extra ingredients or regularization, the expected mass of the Boulware-Deser black hole.