Asymptotically anti-de Sitter spacetimes in topologically massive gravity

Abstract

We consider asymptotically anti-de Sitter spacetimes in three-dimensional topologically massive gravity with a negative cosmological constant, for all values of the mass parameter $\mu$ ($\mu \ne 0$). We provide consistent boundary conditions that accommodate the recent solutions considered in the literature, which may have a slower fall-off than the one relevant for General Relativity. These conditions are such that the asymptotic symmetry is in all cases the conformal group, in the sense that they are invariant under asymptotic conformal transformations and that the corresponding Virasoro generators are finite. It is found in particular that at the chiral point $|\mu l|=1$ (where $l$ is the anti-de Sitter radius), one must allow for logarithmic terms (absent for General Relativity) in the asymptotic behaviour of the metric in order to accommodate the new solutions present in topologically massive gravity, and that these logarithmic terms make both sets of Virasoro generators non-zero even though one of the central charges vanishes.

13 pages, no figures, references and a note added. To be published in PRD (Rapid Communications)

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