The higher dimensional instabilities of AdS in holographic semiclassical gravity

TL;DR

This paper investigates the stability of higher-dimensional AdS black holes with quantum hair in holographic semiclassical gravity, revealing conditions for dynamical and thermodynamic instabilities through perturbation analysis and free energy computations.

Contribution

It constructs new asymptotically AdS black hole solutions with quantum hair in 4 and 5 dimensions and analyzes their stability properties within holographic semiclassical gravity.

Findings

Hyperbolic AdS black holes can be dynamically unstable under certain conditions.

Thermodynamic instability depends on Gauss-Bonnet parameter and can favor hairy solutions.

Quantum hair influences the stability and thermodynamics of higher-dimensional AdS black holes.

Abstract

In the framework of AdS/CFT duality, we consider the semiclassical problem in general quadratic theory of gravity. We construct asymptotically global AdS and hyperbolic~(topological) AdS black hole solutions with non-trivial quantum hair in $4$ and $5$-dimensions by perturbing the maximally symmetric AdS solutions to the holographic semiclassical equations. We find that under certain conditions, our semiclassical solution of hyperbolic AdS black holes can be dynamically unstable against linear perturbations. In this holographic semiclassical context, we also study the thermodynamic instability of the hairy solutions in the $5$-dimensional Gauss-Bonnet theory by computing the free energy and show that depending on the parameter of the Gauss-Bonnet theory, the free energy can be smaller than that of the background maximally symmetric AdS solution in both the global AdS and hyperbolic AdS black hole cases.