Abstract
We investigate the asymptotic structure of the three dimensional warped anti de sitter black holes in the Bergshoeff, Hohm and Townsend massive gravity using the canonical Hamiltonian formalism. We define the canonical asymptotic guage generators, which produce the conserved charges and the asymptotic symmetry group for the warped anti de sitter black holes. The attained symmetry group is described by a semi direct sum of a Virasoro and a KacMoody 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 warped anti de sitter black holes. We also show that the black hole entropy obeys the Cardy formula of the dual conformal field theory .
Highlights
A theoretically physical issue in general relativity (GR) is the existence of black hole solutions, which are naturally endowed through the laws of black hole thermodynamics and accompanied by a macroscopic entropy [1,2]
We study the BHT massive gravity in the canonical first-order formalism [18] on the basis of WAdS3 black holes, which have introduced in Refs. [19] and [20]
We have studied the WAdS3 black hole in the 3D BHT massive gravity and found its properties in the view point of the AdS/conformal field theory (CFT) correspondence
Summary
A theoretically physical issue in general relativity (GR) is the existence of black hole solutions, which are naturally endowed through the laws of black hole thermodynamics and accompanied by a macroscopic entropy [1,2]. The BHT massive gravity theory is a unitary parity-preserving extension, which includes higher curvature terms up to the forth order of derivatives [13] Other extensions of this theory could be found in Refs. The Poisson bracket(PB) algebra of the asymptotic generators describe the asymptotic symmetry group (ASG) of the asymptotically warped backgrounds in the BHT massive gravity We show that these conserved charges satisfy the black hole mechanics as the first law, the Smarr formula [23], and the Cardy formula [24] in verification of the AdS/CFT correspondence. After having briefly discussed the canonical structure of the BHT massive gravity, we will compute the asymptotic conserved charges using the asymptotic gauge generators in Sect.
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