Surface terms and the Gauss-Bonnet Hamiltonian

TL;DR

This paper derives a simple, background-independent expression for the gravitational Hamiltonian with Gauss-Bonnet terms, emphasizing surface contributions and their role in defining spacetime energy.

Contribution

It provides a new derivation of the gravitational Hamiltonian including surface terms using orthonormal frames, applicable to various backgrounds and symmetries.

Findings

Surface terms lead to a simple total energy expression.

The derived energy expression aligns with previous results in specific cases.

Method is flexible for different backgrounds and symmetries.

Abstract

We derive the gravitational Hamiltonian starting from the Gauss-Bonnet action, keeping track of all surface terms. This is done using the language of orthonormal frames and forms to keep things as tidy as possible. The surface terms in the Hamiltonian give a remarkably simple expression for the total energy of a spacetime. This expression is consistent with energy expressions found in hep-th/0212292. However, we can apply our results whatever the choice of background and whatever the symmetries of the spacetime.