Radial Oscillations of Scalar Hair in Black Hole Bombs

TL;DR

This paper investigates the nonlinear dynamics of scalar hair oscillations in black hole bombs, revealing frequency dependence on gauge coupling and identifying critical charge thresholds for instability onset.

Contribution

It uncovers the oscillation patterns of scalar hair and their dependence on gauge coupling, advancing understanding of nonlinear black hole bomb mechanisms.

Findings

Scalar hair exhibits identical oscillation patterns during evolution.

Oscillation frequency depends linearly on gauge coupling constant.

Critical initial charge distinguishes between triggering and non-triggering solutions.

Abstract

Recent research has revealed a novel nonlinear mechanism, distinct from the linear superradiant instability, which triggers the black hole bomb phenomenon. Introducing a massive complex scalar field with nonlinear self-interactions drives the Reissner-Nordstr\"om black hole to shed substantial energy, thereby triggering a black hole bomb. Radial oscillations in the scalar hair profile are observed during this process. In this paper, we further reveal that physical quantities associated with scalar hair exhibit identical oscillation patterns during the evolution of the black hole-scalar field system. Moreover, the oscillation frequency exhibits a linear dependence on the gauge coupling constant of the scalar field with other parameters fixed. Meanwhile, the horizon radius of hairy black holes and the mass within the horizon increase monotonically with the gauge coupling constant. We have also identified a critical initial charge value that distinguishes hairy solutions that trigger black hole bombs from those that do not.