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Asymptotically Anti-de Sitter spacetimes and their stress energy tensor

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arxiv hep-th/0010138 v1 pith:Z67NKTI6 submitted 2000-10-17 hep-th

Asymptotically Anti-de Sitter spacetimes and their stress energy tensor

classification hep-th
keywords actionon-shellenergyrenormalizedstresstensoranti-deboundary
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We consider asymtotically anti-de Sitter spacetimes in general dimensions. We review the origin of infrared divergences in the on-shell gravitational action, and the construction of the renormalized on-shell action by the addition of boundary counterterms. In odd dimensions, the renormalized on-shell action is not invariant under bulk diffeomorphisms that yield conformal transformations in the boundary (holographic Weyl anomaly). We obtain formulae for the gravitational stress energy tensor, defined as the metric variation of the renormalized on-shell action, in terms of coefficients in the asymptotic expansion of the metric near infinity. The stress energy tensor transforms anomalously under bulk diffeomorphisms broken by infrared divergences.

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Cited by 3 Pith papers

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  2. Positivity of holographic energy

    gr-qc 2026-04 unverdicted novelty 6.0

    Positivity of a weighted holographic energy is proven for 4D spacetimes with negative cosmological constant and conformally static boundaries of spherical or toroidal topology with compatible spin structure.

  3. Positivity of holographic energy

    gr-qc 2026-04 unverdicted novelty 5.0

    Positivity is proven for a weighted holographic energy in 4D asymptotically AdS spacetimes with conformally static boundaries of spherical or toroidal topology.