Extended Holographic Rényi Entropy and hyperbolic black hole with scalar hair

Abstract

We study the extended thermodynamics of the hyperbolic black hole with scalar hair and obtain the extended holographic Rényi entropy of holographic conformal field theories with scalar hair. We analyze the behaviors of the extended holographic Rényi entropy in terms of holographic calculations. Moreover, we generalize the capacity of entanglement from the extended Rényi entropy and show that it maps to the heat capacity of the thermal conformal field theories on the hyperbolic space.

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