Nonlinear Evolution of unstable Charged de Sitter Black Holes with Hyperboloidal Formalism

TL;DR

This paper investigates the nonlinear evolution of charged de Sitter black holes under scalar field perturbations using hyperboloidal formalism, revealing superradiance-induced instability and eventual dissipation of the scalar field.

Contribution

It introduces a nonlinear numerical simulation within the hyperboloidal framework to study superradiance instability in charged de Sitter black holes.

Findings

Scalar field grows exponentially during early stages

Superradiance extracts charge from the black hole

Scalar field dissipates, leaving a bald black hole

Abstract

Based on the hyperboloidal framework, we research the dynamical process of charged de Sitter black holes scattered by a charged scalar field. From the linear perturbation analysis, with the coupling strength within a critical interval, the charged scalar field with a superradiance frequency can induce the instability of the system. To reveal the real-time dynamics of such an instability, the nonlinear numerical simulation is implemented. The results show that the scalar field grows exponentially in the early stages and drastically extracts the charge from the black hole due to the superradiance, analogous to the charged black hole in a closed system. Differently, after saturation, the scalar field can not coexist with the central black hole stably and dissipates beyond the cosmological horizon slowly, leaving behind a bald black hole.