A scalar field condensation instability of rotating anti-de Sitter black holes

TL;DR

This paper investigates the instability caused by scalar field condensation in near-extreme rotating anti-de Sitter black holes, revealing new nonlinear solutions and stability conditions through numerical and analytical methods.

Contribution

It extends the understanding of scalar condensation instabilities to rotating and hyperbolic AdS black holes, providing numerical solutions and stability analysis.

Findings

Instability occurs in near-extreme rotating AdS black holes.

Numerical solutions for nonlinear hairy black holes are obtained.

Stability depends on the effective mass respecting the near-horizon BF bound.

Abstract

Near-extreme Reissner-Nordstrom-anti-de Sitter black holes are unstable against the condensation of an uncharged scalar field with mass close to the Breitenlohner-Freedman bound. It is shown that a similar instability afflicts near-extreme large rotating AdS black holes, and near-extreme hyperbolic Schwarzschild-AdS black holes. The resulting nonlinear hairy black hole solutions are determined numerically. Some stability results for (possibly charged) scalar fields in black hole backgrounds are proved. For most of the extreme black holes we consider, these demonstrate stability if the ``effective mass" respects the near-horizon BF bound. Small spherical Reissner-Nordstrom-AdS black holes are an interesting exception to this result.