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

Understand

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.