Thermodynamics in Black-hole/CFT Correspondence

Abstract

The area law of Bekenstein-Hawking entropy of the black hole suggests that the black hole should have a lower-dimensional holographic description. It has been found recently that a large class of rotating and charged black holes could be holographically described a two-dimensional (2D) conformal field theory (CFT). We show that the universal information of the dual CFT, including the central charges and the temperatures, is fully encoded in the thermodynamics laws of both outer and inner horizons. These laws, characterizing how the black hole responds under the perturbation, allows us to read different dual pictures with respect to different kinds of perturbations. The remarkable effectiveness of this thermodynamics method suggest that the inner horizon could play a key role in the study of holographic description of the black hole.

8 pages. Essay awarded honourable mention in the Gravity Research Foundation 2013 Awards for Essays on Gravitation

References in corpus (7)

• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter in Einstein-Maxwell theory
• Inner Mechanics of 3d Black Holes
• Twofold Hidden Conformal Symmetries of the Kerr-Newman Black Hole
• The inner Cauchy horizon of axisymmetric and stationary black holes with surrounding matter
• Black Hole Monodromy and Conformal Field Theory
• Electromagnetic Duality in Dyonic RN/CFT Correspondence

Cited by in corpus (5)

• Phase Transitions in Warped AdS${}_3$ Gravity
• The Universal Property of the Entropy Sum of Black Holes in All Dimensions
• The Entropy Sum of (A)dS Black Holes in Four and Higher Dimensions
• Thermodynamic relations for entropy and temperature of multi-horizons black holes
• Universal entropy relations: entropy formulae and entropy bound