More on Asymptotically Anti-de Sitter Spaces in Topologically Massive Gravity

TL;DR

This paper explores the boundary conditions for asymptotically AdS spacetimes in topologically massive gravity, showing that previous conditions are optimal for maintaining conformal symmetry and analyzing the behavior of different chiralities.

Contribution

It demonstrates that boundary conditions allowing both chiralities simultaneously are incompatible with conformal symmetry below the chiral point.

Findings

Boundary conditions are optimal for conformal invariance.

Only one chirality can be included at a time below the chiral point.

General formulas for asymptotic charges are provided for all topological masses.

Abstract

Recently, the asymptotic behaviour of three-dimensional anti-de Sitter gravity with a topological mass term was investigated. Boundary conditions were given that were asymptotically invariant under the two-dimensional conformal group and that included a fall-off of the metric sufficiently slow to consistently allow pp-wave type of solutions. Now, pp-waves can have two different chiralities. Above the chiral point and at the chiral point, however, only one chirality can be considered, namely the chirality that has the milder behaviour at infinity. The other chirality blows up faster than AdS and does not define an asymptotically AdS spacetime. By contrast, both chiralities are subdominant with respect to the asymptotic behaviour of AdS spacetime below the chiral point. Nevertheless, the boundary conditions given in the earlier treatment only included one of the two chiralities (which could be either one) at a time. We investigate in this paper whether one can generalize these boundary conditions in order to consider simultaneously both chiralities below the chiral point. We show that this is not possible if one wants to keep the two-dimensional conformal group as asymptotic symmetry group. Hence, the boundary conditions given in the earlier treatment appear to be the best possible ones compatible with conformal symmetry. In the course of our investigations, we provide general formulas controlling the asymptotic charges for all values of the topological mass (not just below the chiral point).