Topological invariants and the definition of energy in quadratic gravity theory

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.

arXiv comment11 pages, no figures; references added and few clarifying comments; version accepted for publication in PRD

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• A Komar-like integral for mass and angular momentum of asymptotically AdS black holes in Einstein gravity
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• Vector-tensor gravity from a broken gauge symmetry
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• Energy of anti-de Sitter black holes in odd-dimensional Quadratic Curvature Gravity