Note on Thermodynamics Method of Black Hole/CFT Correspondence

Abstract

In the paper we further refine the thermodynamics method of black hole/CFT correspondence. We show that one can derive the central charges of different holographic pictures directly from the entropy product $S_{+}{S}_{-}$ if it is mass-independent, for a black hole in the Einstein gravity or the gravity without diffeomorphism anomaly. For a general black hole in the Einstein gravity that admits holographic descriptions, we show that the thermodynamics method and asymptotic symmetry group (ASG) analysis can always give consistent results in the extreme limit. Furthermore, we discuss the relation between black hole thermodynamics and the hidden conformal symmetry. We show that the condition $T_{+}{A}_{+}=T_{-}{A}_{-}$, with $A_{\pm }$ being the outer and inner horizon areas, is the necessary, but not sufficient, condition for a black hole to have the hidden conformal symmetry. In particular, for the Einstein(-Maxwell) gravity $T_{+}{A}_{+}=T_{-}{A}_{-}$ is just the condition $T_{+}{S}_{+}=T_{-}{S}_{-}$, with $S_{\pm }$ being the outer and inner horizon entropies, which is the condition for the entropy product $S_{+}{S}_{-}$ being mass-dependent. When there exists the hidden conformal symmetry in the low-frequency scattering off the generic non-extremal black hole, it always leads to the same temperatures of dual CFT as the ones got from the thermodynamics method.

31 pages, references added, published version

References in corpus (13)

• Surface charge algebra in gauge theories and thermodynamic integrability
• CFT Duals for Extreme Black Holes
• Kerr-AdS/CFT Correspondence in Diverse Dimensions
• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Cargese Lectures on the Kerr/CFT Correspondence
• Greybody Factors and Charges in Kerr/CFT
• Holographic Duals of Kaluza-Klein Black Holes
• The Kerr/CFT Correspondence and String Theory
• Twofold Hidden Conformal Symmetries of the Kerr-Newman Black Hole
• Note on Thermodynamics Method of Black Hole/CFT Correspondence
• Hidden Conformal Symmetry of Extremal Black Holes
• Holographic Descriptions of Black Rings
• RN/CFT Correspondence From Thermodynamics

Cited by in corpus (1)

• Note on Thermodynamics Method of Black Hole/CFT Correspondence