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

TL;DR

This paper establishes consistent boundary conditions for warped AdS_3 spaces in topologically massive gravity, analyzing their asymptotic charges and algebra, and comparing with Brown-Henneaux conditions.

Contribution

It introduces boundary conditions for warped AdS_3 spaces, demonstrating finite, conserved charges with Virasoro and current algebra structures, and explores their relation to Brown-Henneaux conditions.

Findings

Asymptotic charges form a Virasoro and current algebra

Charges are finite, conserved, and integrable

Energy of boundary excitations varies with spacelike/timelike cases

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.