Late-Time Evolution of Charged Gravitational Collapse and Decay of Charged Scalar Hair - II

TL;DR

This paper analytically investigates how charged scalar fields decay around charged black holes, revealing the mechanisms behind the loss of scalar hair and implications for black hole stability.

Contribution

It extends previous spectral decomposition methods to analyze charged scalar perturbations and details their decay behavior in Reissner-Nordström spacetime.

Findings

Charged perturbations decay as inverse power-law at infinity.

Oscillatory inverse power-law decay occurs along the outer horizon.

Charged black holes shed their scalar hair more slowly than neutral ones.

Abstract

We study analytically the initial value problem for a charged massless scalar-field on a Reissner-Nordstr\"om spacetime. Using the technique of spectral decomposition we extend recent results on this problem. Following the no-hair theorem we reveal the dynamical physical mechanism by which the charged hair is radiated away. We show that the charged perturbations decay according to an inverse power-law behaviour at future timelike infinity and along future null infinity. Along the future outer horizon we find an oscillatory inverse power-law relaxation of the charged fields. We find that a charged black hole becomes ``bald'' slower than a neutral one, due to the existence of charged perturbations. Our results are also important to the study of mass-inflation and the stability of Cauchy horizons during a dynamical gravitational collapse of charged matter in which a charged black-hole is formed.