A boundary stress tensor for higher-derivative gravity in AdS and Lifshitz backgrounds

TL;DR

This paper develops a generalized boundary stress tensor for higher-derivative gravity theories in AdS and Lifshitz backgrounds, enabling finite physical quantities and new insights into black hole solutions and dual field theories.

Contribution

It introduces a universal method to define a well-posed boundary stress tensor for curvature-squared gravities, including Lifshitz backgrounds, with new counterterms and applications to black hole physics.

Findings

Finite results for physical parameters in AdS with counterterms

Derived known and new central charges and black hole masses

Proposed a covariant counterterm for Lifshitz backgrounds

Abstract

We investigate the Brown-York stress tensor for curvature-squared theories. This requires a generalized Gibbons-Hawking term in order to establish a well-posed variational principle, which is achieved in a universal way by reducing the number of derivatives through the introduction of an auxiliary tensor field. We examine the boundary stress tensor thus defined for the special case of `massive gravity' in three dimensions, which augments the Einstein-Hilbert term by a particular curvature-squared term. It is shown that one obtains finite results for physical parameters on AdS upon adding a `boundary cosmological constant' as a counterterm, which vanishes at the so-called chiral point. We derive known and new results, like the value of the central charges or the mass of black hole solutions, thereby confirming our prescription for the computation of the stress tensor. Finally, we inspect recently constructed Lifshitz vacua and a new black hole solution that is asymptotically Lifshitz, and we propose a novel and covariant counterterm for this case.