Note on Thermodynamics Method of Black Hole/CFT Correspondence

Understand

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.