Nonlinear Evolution and Final Fate of Charged Anti-de Sitter Black Hole Superradiant Instability

TL;DR

This paper investigates the nonlinear evolution of superradiant instability in charged AdS black holes, showing how scalar fields grow, extract charge, and lead to stable hairy black holes, with implications for black hole superradiance.

Contribution

It provides a detailed nonlinear analysis of superradiant instability in charged AdS black holes, including the formation of stable hairy black holes and charge extraction dynamics.

Findings

Superradiant perturbations grow initially as predicted by linear theory.

Black holes lose charge and mass, ending in stable hairy black holes.

Large gauge coupling results in significant charge extraction and entropy increase.

Abstract

We describe the full nonlinear development of the superradiant instability for a charged massless scalar field, coupled to general relativity and electromagnetism, in the vicinity of a Reissner-Nordstrom-AdS black hole. The presence of the negative cosmological constant provides a natural context for considering perfectly reflecting boundary conditions and studying the dynamics as the scalar field interacts repeatedly with the black hole. At early times, small superradiant perturbations grow as expected from linearized studies. Backreaction then causes the black hole to lose charge and mass until the perturbation becomes nonsuperradiant, with the final state described by a stable hairy black hole. For large gauge coupling, the instability extracts a large amount of charge per unit mass, resulting in greater entropy increase. We discuss the implications of the observed behavior for the general problem of superradiance in black hole spacetimes.