Energy in Higher-Derivative Gravity via Topological Regularization

TL;DR

This paper introduces a new, intrinsically non-linear method to define gravitational energy in higher-derivative gravity theories with AdS boundary conditions, using topological invariants to regularize charges and ensure well-posed variational problems.

Contribution

It extends topological regularization techniques to higher-derivative gravity, providing a novel way to compute conserved charges consistent with previous methods.

Findings

Successfully computed energy and angular momentum of Schwarzschild-AdS black holes.

Results agree with previous methods, validating the approach.

Extended the method to gravitational waves in AdS, confirming consistency.

Abstract

We give a novel definition of gravitational energy for an arbitrary theory of gravity including quadratic-curvature corrections to Einstein equations. We focus on the theory in four dimensions, in presence of negative cosmological constant, and with asymptotically anti-de Sitter (AdS) boundary conditions. As a first example, we compute the gravitational energy and angular momentum of Schwarzschild-AdS black holes, for which we obtain results consistent with previous computations performed using different methods. However, our method differs qualitatively from other ones in the feature of being intrinsically non-linear. It relies on the idea of adding to the gravity action topological invariant terms which suffice to regularize the Noether charges and render the variational problem well-posed. This is an idea that has been previously considered in the case of second-order theories, such as general relativity and which, as shown here, extends to higher-derivative theories. Besides black holes, we consider other solutions, such as gravitational waves in AdS, for which we also find results in agreement. This enables us to investigate the consistency of this approach in the non-Einstein sector of the theory.