Lorentz-diffeomorphism quasi-local conserved charges and Virasoro algebra in Chern-Simons-like theories of gravity

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• 作者：M.R. Setare ; ^{rezakord@ipm.ir" class="auth_mail" title="E-mail the corresponding author} ; H. Adami ^{hamed.adami@yahoo.com" class="auth_mail" title="E-mail the corresponding author}
• 刊名：Nuclear Physics B
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：909
• 期：Complete
• 页码：345-359
• 全文大小：301 K

文摘

The Chern–Simons-like theories of gravity (CSLTG) are formulated at first order formalism. In this formalism, the derivation of the entropy of a black hole on bifurcation surface, as a quasi-local conserved charge is problematic. In this paper we overcome these problems by considering the concept of total variation and the Lorentz–Lie derivative. We firstly find an expression for the ADT conserved current in the context of the CSLTG which is based on the concept of the Killing vector fields. Then, we generalize it to be conserved for all diffeomorphism generators. Thus, we can extract an off-shell conserved charge for any vector field which generates a diffeomorphism. The formalism presented here is based on the concept of quasi-local conserved charges which are off-shell. The charges can be calculated on any codimension two space-like surface surrounding a black hole and the results are independent of the chosen surface. By using the off-shell quasi-local conserved charge, we investigate the Virasoro algebra and find a formula to calculate the central extension term. We apply the formalism to the BTZ black hole solution in the context of the Einstein gravity and the Generalized massive gravity, then we find the eigenvalues of their Virasoro generators as well as the corresponding central charges. Eventually, we calculate the entropy of the BTZ black hole by the Cardy formula and we show that the result exactly matches the one obtained by the concept of the off-shell conserved charges.