A scalar field instability of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time

TL;DR

This paper investigates the stability of 4+1 dimensional Anti-de Sitter black holes with spherical horizons, revealing a scalar field instability that leads to new hairy black hole solutions and models a holographic phase transition.

Contribution

It demonstrates a non-linear instability due to scalar field condensation and constructs new hairy black hole solutions in higher-dimensional AdS space.

Findings

Scalar field condensation causes instability in black holes.

Constructed hairy black hole solutions with scalar hair.

Described a holographic superconductor phase transition.

Abstract

We study the stability of static as well as of rotating and charged black holes in (4+1)-dimensional Anti-de Sitter space-time which possess spherical horizon topology. We observe a non-linear instability related to the condensation of a charged, tachyonic scalar field and construct "hairy" black hole solutions of the full system of coupled Einstein, Maxwell and scalar field equations. We observe that the limiting solution for small horizon radius is either a hairy soliton solution or a singular solution that is not a regular extremal solution. Within the context of the gauge/gravity duality the condensation of the scalar field describes a holographic conductor/superconductor phase transition on the surface of a sphere.