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

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