Abstract
We construct a series of new hyperbolic black hole solutions in Einstein–Scalar system and we apply holographic approach to investigate the spherical Rényi entropy in various deformations of dual conformal field theories (CFTs). Especially, we introduce various powers of scalars in the scalar potentials for massive and massless scalar. These scalar potentials correspond to deformation of dual CFTs. Then we solve asymptotically hyperbolic AdS black hole solutions numerically. We map the instabilities of these black hole solutions to phase transitions of field theory in terms of CHM mapping between hyperbolic hairy AdS black hole and spherical Rényi entropy in dual field theories. Based on these solutions, we study the temperature dependent condensation of dual operator of massive and massless scalar respectively. These condensations show that there might exist phase transitions in dual deformed CFTs. We also compare free energy between asymptotically hyperbolic AdS black hole solutions and hyperbolic AdS Schwarz (AdS-SW) black hole to test phase transitions. In order to confirm the existence of phase transitions, we turn on linear in-homogeneous perturbation to test stability of these hyperbolic hairy AdS black holes. In this paper, we show how potential parameters affect the stability of hyperbolic black holes in several specific examples. For general values of potential parameters, it needs further study to see how the transition happens. Finally, we comment on these instabilities associated with spherical Rényi entropy in dual deformed CFTs.
Highlights
We will focus on the instability of hyperbolic AdS black holes and comment on holographic Renyi entropy
Motivated by studying entanglement Renyi entropy (ERE) with spherical entangling surface in deformed CFTs, we work out the background with introducing series powers of neutral scalar in scalar potential
We just compare free energy between the new hyperbolic AdS solutions and hyperbolic AdS-SW solution to check the stability of these solutions
Summary
G5 is the 5D Newton constant, g is the 5D metric determinant and φ, V are the scalar field and the corresponding potential. We would like to choose the following ansatz to solve the Einstein equations of motion, ds. In terms of the above ansatz, one can obtain equations, φ′′(z) +. (2.5) is not independent on the other three equations in (2.4). Once the gravity solution is obtained from (2.4), one could use (2.5) to check the solution. We note that (2.4) would impose a natural boundary condition near horizon. If one collects all the terms with a denominator f (z), the results are as following. Since the horizon is not a real singularity, the apparent singularity f (zh) = 0 in Eq(2.4) should be canceled by requiring Q(zh) = 0. We will try to solve this boundary value problem using numerical method developed in Ref.[21]
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