https://doi.org/10.1140/epjp/s13360-024-05656-4
Regular Article
Extended holographic Rényi entropy and hyperbolic black hole with scalar hair
School of Physics, Sun Yat-sen University, 510275, Guangzhou, People’s Republic of China
Received:
4
May
2023
Accepted:
12
September
2024
Published online:
1
October
2024
Extended Rényi entropy is a new type of generalization of the usual Rényi entropy that can relate to a thermodynamic quantity. In this paper, we first study the extended thermodynamics of the hyperbolic black holes with scalar hair. The result shows that there are no van der Waals behaviors for the hairy hyperbolic AdS black hole. We extend the description of holographic Rényi entropy of holographic conformal field theories with scalar hair. We show that the extended holographic Rényi entropy presents a transition at critical parameters when the black hole has a thermodynamic phase transition at a critical temperature. The inequalities of extended holographic Rényi entropy are satisfied in our holographic calculations. We also holographically compute the conformal dimension of twist operators in terms of gravitational quantities. 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. We also show that the extended holographic capacity of entanglement has a jump when the black hole has a zeroth-order phase transition.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
