Effects of nonlinear interactions on the superradiant instability of charged black holes

TL;DR

This work investigates nonlinear superradiant growth of a charged axion field around a Reissner-Nordström black hole enclosed in a reflecting cavity, using full nonlinear numerical relativity. The model couples the axion to electromagnetism with a potential $V(\phi)$ controlled by the mass $m$ and decay constant $f_a$, and explores a broad parameter space including $\bar{f_a}$, $\bar{q}$, $\bar{m}$, and $r_{\text{mirr}}$. The key finding is that axion nonlinearities bifurcate the instability into two regimes near $\bar{f_a} \sim 0.01$, enabling diverse dynamical endpoints such as hairy black holes, long-lived oscillations, and Bosenova events, with energy and charge extraction strongly modulated by $\bar{m}$ and cavity size. These results reveal a rich, degenerate-like parameter landscape with implications for ultralight dark matter around black holes and motivate extensions to Kerr spacetimes and observational signatures.

Abstract

A Reissner-Nordström black hole (RNBH) enclosed in a cavity is known to be superradiantly unstable to charged scalar perturbations below a critical frequency. Inspired by the emergence of the QCD axion as a prominent dark matter candidate, we construct a model featuring an axion field coupled to an electromagnetic field that undergoes superradiant growth around an RNBH. Utilizing numerical relativity, we achieve stable, long-term evolution of this system and perform a comparative analysis across various parameter spaces. Our comprehensive investigation reveals the formation of a hairy black hole, whose final state is governed by a diverse set of physical parameters. Notably, the decay constant in the axion potential, representing nonlinear interactions, bifurcates the superradiant instability into two distinct behavioral regimes, leading to more significant dynamical shifts than previously reported. Furthermore, we examine the influence of the scalar field's charge and mass, as well as the mirror's position. We investigate the axionic bosenova process and observe a long-term beating pattern of the axion field induced by nonlinear interactions. By fine-tuning these parameter combinations, we demonstrate that the system can evolve toward a variety of distinct physical endpoints.

Figures (19)

• Figure 1: Energy evolution of the axion field for various mass parameters within a cavity of radius $r_{\text{mirr}}=20M$. The parameters are set to $\bar{f_a}\to\infty$ and $\bar{q}=20$.
• Figure 2: Energy evolution of the axion field for various decay constants $\bar{f_a}$ and $\bar{q}$ within a cavity of radius $r_{\text{mirr}}=10M$. The parameter is set to $\bar{m}=0.2$.
• Figure 3: Charge transfer between the axion field and the black hole for various decay constants $\bar{f_a}$ and $\bar{q}$ within a cavity of radius $r_{\text{mirr}}=10M$. Dashed and solid lines denote the charges of the black hole and the axion field, respectively. The parameter is set to $\bar{m}=0.2$.
• Figure 4: Energy evolution of the axion field for various decay constants $\bar{f_a}$ and $\bar{q}$ within a cavity of radius $r_{\text{mirr}}=15M$. The parameter is set to $\bar{m}=0.2$.
• Figure 5: Charge transfer between the axion field and the black hole for various decay constants $\bar{f_a}$ and $\bar{q}$ within a cavity of radius $r_{\text{mirr}}=15M$. Dashed and solid lines denote the charges of the black hole and the axion field, respectively. The parameter is set to $\bar{m}=0.2$.