Asymptotically anti-de Sitter spacetimes in topologically massive gravity

TL;DR

This paper explores the boundary conditions and asymptotic symmetries of three-dimensional topologically massive gravity in anti-de Sitter space, revealing the necessity of logarithmic terms at the chiral point and their impact on the Virasoro algebra.

Contribution

It establishes consistent boundary conditions for all mass parameters in topologically massive gravity, including the chiral point, and analyzes the resulting asymptotic symmetry algebra.

Findings

Boundary conditions compatible with recent solutions.

Logarithmic terms are necessary at the chiral point.

Virasoro generators remain non-zero despite one vanishing central charge.

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 $\mu$ ($\mu\neq0$). 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.