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

TL;DR

This paper explores the thermodynamics of AdS black holes and their dual CFTs, deriving a modified Friedmann equation and analyzing entropy corrections related to the central charge in the AdS/CFT framework.

Contribution

It introduces a modified Friedmann equation derived from the Smarr formula and interprets the logarithmic central charge term as black hole entropy within AdS/CFT.

Findings

Logarithmic correction to Hawking-Bekenstein entropy depending on central charge

AdS radius identified as the critical shadow radius

Real gas in AdS dual to ideal gas in CFT

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.