Dynamical spontaneous scalarization in Einstein-Maxwell-scalar theory

TL;DR

This paper investigates the linear instability and nonlinear evolution of Reissner-Nordström black holes in Einstein-Maxwell-scalar theory, revealing how scalarization occurs dynamically and the dominant modes involved.

Contribution

It provides a detailed analysis of the dynamical process of spontaneous scalarization in charged black holes within Einstein-Maxwell-scalar theory, including both linear and nonlinear stages.

Findings

Scalar field evolution is dominated by the fundamental unstable mode during early times.

Late-time evolution approaches scalarized black hole solutions as nonlinear perturbations.

The coupling function $f()=e^{-b^2}$ admits both scalar-free and scalarized solutions.

Abstract

We study the linear instability and the nonlinear dynamical evolution of the Reissner-Nordstr\"om (RN) black hole in the Einstein-Maxwell-scalar theory in asymptotic flat spacetime. We focus on the coupling function $f(\phi)=e^{-b\phi^2}$ which allows both the scalar-free RN solution and scalarized black hole solution. We first present the evolution of system parameters during dynamic scalarization. For parameter regions where spontaneous scalarization occurs, we find that the evolution of the scalar field at the horizon is dominated by the fundamental unstable mode from linear analysis at early times. At late times, the nonlinear evolution can be viewed as the perturbation of scalarized black holes.