Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity

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.

16 pages. v3: title and presentation updated to match published version. Explicit expressions for 4th-order Lovelock Lagrangians and Gibbons-Hawking terms can be found in v2

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• A Novel Derivation of the Boundary Term for the Action in Lanczos-Lovelock Gravity
• Counterterms, critical gravity and holography
• Higher-derivative holography with a chemical potential
• Null boundary terms for Lanczos-Lovelock gravity
• A Holographic Study of the $a$-theorem and RG Flow in General Quadratic Curvature Gravity
• Universal renormalization procedure for higher curvature gravities in D$\le$5
• Non-analyticity of holographic Rényi entropy in Lovelock gravity
• Quasi-local energy and ADM mass in pure Lovelock gravity
• Higher-Curvature Gravity, Black Holes and Holography
• Counterterms for Static Lovelock Solutions