Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity

Details Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity Simple counterterms for asymptotically AdS spacetimes in Lovelock gravity

2011-07-06

arxiv.org/abs/1107.1250v3

Phys. Rev. D 84, 104036 (2011)

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages. v3: title and presentation updated to match published version. Explicit expressions for 4th-order Lovelock Lagrangia

Scientific paper

10.1103/PhysRevD.84.104036

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.

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