Asymptotically Anti-de Sitter spacetimes and their stress energy tensor

TL;DR

This paper reviews the properties of asymptotically anti-de Sitter spacetimes, focusing on the renormalized gravitational action, holographic stress energy tensor, and their anomalies under boundary conformal transformations.

Contribution

It provides explicit formulae for the holographic stress energy tensor in various dimensions and analyzes its transformation properties under bulk diffeomorphisms.

Findings

Infrared divergences lead to non-invariance of the on-shell action in odd dimensions.

Explicit expressions for the stress energy tensor are derived from asymptotic metric coefficients.

The stress energy tensor exhibits anomalous transformation behavior under broken diffeomorphisms.

Abstract

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.