Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity

TL;DR

This paper develops a straightforward algorithm to generate boundary counterterms up to sixth order in the Riemann tensor for various gravity theories in asymptotically AdS spacetimes, extending previous results.

Contribution

It introduces a simple method to derive counterterms up to sixth order for Einstein-Hilbert, Gauss-Bonnet, and third-order Lovelock gravities in AdS.

Findings

Counterterms up to sixth order are systematically generated.

The method applies to multiple gravity theories including $F(R)$ gravity.

Provides insights into boundary term structures for higher-order gravities.

Abstract

Although gravitational actions diverge in asymptotically AdS spacetimes, boundary counterterms can be added in order to cancel out those divergences; such counterterms are known in general to third order in the Riemann tensor for the Einstein-Hilbert action. Considering foliations of AdS with an $S^m \times H^{d-m}$ boundary, we discuss a simple algorithm which we use to generate counterterms up to sixth order in the Riemann tensor, for the Einstein-Hilbert, Gauss-Bonnet and third-order-Lovelock Lagrangians. We also comment on other theories such as $F(R)$ gravity.