Abstract
We provide a simple method to compute the energy in higher curvature gravity in asymptotically AdS spacetimes in even dimensions. It follows from the combined use of topological terms added to the gravity action, and the Wald charges derived from the augmented action functional. No additional boundary terms are needed. As a consistency check, we show that the formula for the conserved quantities derived in this way yields the correct result for the mass of asymptotically AdS black holes.
Highlights
Higher-curvature corrections to Einstein-Hilbert action are ubiquitous in effective field theory when gravity is involved
In a previous work [33], we have shown that the addition of the Gauss-Bonnet invariant to quadraticcurvature gravity (QCG) action in D 1⁄4 4 acts as a regulator of the Noether charges in both Einstein and nonEinstein sectors of the theory
The above discussion shows the effect of the Euler topological invariant added to the QCG action, which is similar to the one in general relativity (GR) and Einstein-Gauss-Bonnet gravity actions
Summary
Higher-curvature corrections to Einstein-Hilbert action are ubiquitous in effective field theory when gravity is involved. The interest in healthy higher-order corrections to Einstein theory has been renewed. There have been very interesting works studying higher-curvature models in anti-de Sitter (AdS) space. Such is the case of the so-called critical gravity (CG) theories [14,15], which provide ghost-free models of gravity in asymptotically AdS spacetimes in D ≥ 4 dimensions. For instance, the connection between higher-curvature conformally invariant theories and Einstein gravity in (A)dS in D 1⁄4 4 [17]. The computation of conserved charges in highercurvature theories in both asymptotically flat and asymptotically AdS spaces is an important problem that has been addressed by many authors in the last 20 years; notably by
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