Semi-classical central charge in topologically massive gravity

It is shown that the warped black hole geometries discussed recently in arXiv:0807.3040 (Anninos et al 2008) admit an algebra of asymptotic symmetries isomorphic to the semi-direct product of a Virasoro algebra and an algebra of currents. The realization of this asymptotic symmetry by canonical charges allows us to find the central charge of the Virasoro algebra. The right-moving central charge is obtained when the Virasoro generators are normalized in order to have a positive zero-mode spectrum for the warped black holes. If one normalizes the Virasoro generators in order to have a positive central charge, the zero mode is then unbounded from below. The current algebra is also shown to be centrally extended.