Boundary conditions for spacelike and timelike warped AdS_3 spaces in topologically massive gravity

TL;DR

This work derives consistent boundary conditions for spacelike and timelike warped AdS3 spaces within Topologically Massive Gravity, showing that the resulting asymptotic charges comprise a Virasoro algebra plus a current algebra that are finite, integrable, and conserved. By choosing a field-dependent normalization and fixing a T0 sector, the authors can ensure a non-negative Virasoro zero mode and, in the spacelike case, discuss a potential truncation to remove the current algebra from the phase space. They also construct a family of regular solitons in the timelike warped sector and analyze their energy properties, including a mass gap relative to the background. Finally, the paper compares warped boundary conditions to Brown-Henneaux AdS3 conditions, elucidating how the ν^2→1 limit connects to BTZ/Brown-Henneaux structures and clarifying limitations on extending a second Virasoro sector away from ν^2=1.

Abstract

We propose a set of consistent boundary conditions containing the spacelike warped black holes solutions of Topologically Massive Gravity. We prove that the corresponding asymptotic charges whose algebra consists in a Virasoro algebra and a current algebra are finite, integrable and conserved. A similar analysis is performed for the timelike warped AdS_3 spaces which contain a family of regular solitons. The energy of the boundary Virasoro excitations is positive while the current algebra leads to negative (for the spacelike warped case) and positive (for the timelike warped case) energy boundary excitations. We discuss the relationship with the Brown-Henneaux boundary conditions.