A Nonlinear Endpoint of Charged Horizon Instabilities

TL;DR

This paper numerically constructs extremal black holes with scalar hair through nonlinear evolution, revealing universal critical behavior and unbounded curvature growth near the horizon, advancing understanding of charged horizon instabilities.

Contribution

It extends previous work to include charged scalar fields, demonstrating the formation of extremal black holes with hair via nonlinear dynamics and analyzing their critical phenomena.

Findings

Extremal black holes with scalar hair can form dynamically from super-extremal initial conditions.

Near-threshold solutions exhibit universal critical behavior.

Scalar curvature diverges near the horizon, indicating potential for large curvatures without black hole formation.

Abstract

We numerically construct asymptotically extremal black holes through the nonlinear evolution of a charged scalar field. Our procedure -- which extends the work of Murata-Reall-Tanahashi to include charged scalar dynamics -- involves the fine-tuned scattering of wave packets within an initially super-extremal Reissner-Nordstrom spacetime. The resulting extremal solution develops an event horizon along which the energy density diverges and the charge density approaches a constant (i.e., the horizon forms with "hair"). We investigate this behavior from the perspective of critical phenomena in gravitational collapse, giving evidence that dynamical extremal black holes act as universal threshold solutions modulo this family-dependent hair. As in the linear instability of fixed extremal backgrounds, the scalar field decays outside the dynamical extremal horizon. But just inside the horizon, the scalar curvature appears to develop unbounded growth. This implies that near-threshold solutions without a black hole could develop correspondingly large curvatures visible from future null infinity.