Entropy as logarithmic term of the central charge and modified Friedmann equation in AdS/CFT correspondence

Abstract

This paper is about the extended thermodynamics of AdS black holes and its relation to CFT thermodynamics. The logarithmic term of the central charge is interpreted as black hole entropy. We have obtain a modified Friedmann equation from the Smarr formula. We find that the AdS radius is the critical shadow radius. We obtain the Hawking-Bekenstein formula with logarithmic corrections, which depends on the central charge. The real gas in AdS is a dual of an ideal gas in CFT. This work can be extended to the AdS-Kerr black holes.

arXiv comment22 pages, 4 figures

References in corpus (42)

• The Large N Limit of Superconformal Field Theories and Supergravity
• Holographic Derivation of Entanglement Entropy from AdS/CFT
• A Model of Holographic Dark Energy
• Enthalpy and the Mechanics of AdS Black Holes
• Black hole chemistry: thermodynamics with Lambda
• The Kerr/CFT Correspondence
• The Area of a Rough Black Hole
• A holographic proof of the strong subadditivity of entanglement entropy
• Barrow entropic dark energy: A member of generalized holographic dark energy family
• Big Bang Nucleosynthesis constraints on Barrow entropy
• Quasinormal Modes of Black Holes Surrounded by Dark Matter and Their Connection with the Shadow Radius
• Holographic Thermodynamics Requires a Chemical Potential for Color
• The generalized second law of thermodynamics with Barrow entropy
• Thermodynamics of AdS Black Holes: Central Charge Criticality
• Photon orbits and thermodynamic phase transition of $d$-dimensional charged AdS black holes
• Bose condensation and branes
• Charged BTZ black holes in the context of massive gravity's rainbow
• Quantum gravity effects on Hořava-Lifshitz black hole
• Restricted phase space thermodynamics for AdS black holes via holography
• Kinetics of a phase transition for a Kerr-AdS black hole on the free-energy landscape
• Thermodynamic geometry of a black hole surrounded by perfect fluid in Rastall theory
• Quantum corrections to thermodynamics of quasitopological black holes
• Constraints on Barrow entropy from M87* and S2 star observations
• Thermal fluctuations of charged black holes in gravity's rainbow
• Thermal Fluctuations in a Hyperscaling Violation Background
• Leading-order corrections to charged rotating AdS black holes thermodynamics
• Perturbed thermodynamics of charged black hole solution in Rastall theory
• Modified cosmology through Barrow entropy
• Logarithmic corrected Van der Waals black holes in higher dimensional AdS space
• Thermodynamics of Higher Order Entropy Corrected Schwarzschild-Beltrami-de Sitter Black Hole
• Phase transition of a charged AdS black hole with a global monopole through geometrical thermodynamics
• Perturbed thermodynamics and thermodynamic geometry of a static black hole in $f(R)$ gravity
• Black hole thermodynamics is extensive with variable Newton constant
• Thermal fluctuations to thermodynamics of non-rotating BTZ black hole
• Where are the black hole entropy degrees of freedom ?
• Thermodynamics for higher dimensional rotating black holes with variable Newton constant
• Lux in obscuro II: Photon Orbits of Extremal AdS Black Holes Revisited
• Accretion disks around a static black hole in $f(R)$ gravity
• Quantum corrected thermodynamics and $P-V$ criticality of self-gravitating Skyrmion black holes
• An attempt to add Barrow entropy in $f(R)$ gravity
• Holographic dark energy satisfying the energy conditions in Lovelock gravity
• The Special Role of Toroidal Black Holes in Holography

Cited by in corpus (1)

• Black Hole Chemistry: the first 15 years