Boundary conditions for spacelike and timelike warped AdS3 spaces in topologically massive gravity

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 AdS3 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. Pacs: 04.20.-q,04.60.-m,04.70.-s,11.30.-j Topologically Massive Gravity [1, 2] (TMG) has recently received a great deal of attention since the conjecture by Li, Song and Strominger [3] that the theory is chiral at a particular point in parameter space. Although counter-arguments to the original proposal appeared (regarding chirality and unitarity) [4, 5, 6, 7], it was shown that a refined version of the conjecture remains intact upon truncating the non-chiral degree of freedom, which in turn could lead to a consistent quantum theory [8]. It has also been known since the work of [1, 2] that AdS3 space is an unstable background solution of TMG with Lagrangian