Canonical structure of BHT massive gravity in warped AdS3 sector

We investigate the asymptotic structure of the three dimensional Warped Anti-de Sitter (WAdS3) black holes in the Bergshoeff–Hohm–Townsend (BHT) massive gravity using the canonical Hamiltonian formalism. We define the canonical asymptotic gauge generators, which produce the conserved charges and the asymptotic symmetry group for the WAdS3 black holes. The attained symmetry group is described by a semi-direct sum of a Virasoro and a Kač–Moody algebra. Using the Sugawara construction, we obtain a direct sum of two Virasoro algebras. We show that not only the asymptotic conserved charges satisfy the first law of black hole thermodynamics, but also they lead to the expected Smarr formula for the WAdS3 black holes. We also show that the black hole's entropy obeys the Cardy formula of the dual conformal field theory (CFT).