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

TL;DR

This paper analytically investigates how charged scalar fields decay around a charged black hole, revealing slower decay of charged hair compared to neutral, with implications for black hole stability and mass inflation.

Contribution

It provides a detailed analytical description of the late-time decay of charged scalar fields in Reissner-Nordström spacetime, highlighting differences from neutral cases and implications for black hole physics.

Findings

Charged fields decay via inverse power-law at infinity.

Charged hair decays slower than neutral hair.

Results impact understanding of black hole stability and mass inflation.

Abstract

We study analytically the asymptotic evolution of charged fields around a Reissner-Nordstr\"om black-hole. Following the no-hair theorem we focus attention on the dynamical mechanism by which the charged hair is radiated away. We find an inverse power-law relaxation of the charged fields at future timelike infinity, along future null infinity and an oscillatory inverse power-law relaxation along the future outer horizon. We show that a charged hair is shedd slower than a neutral one. Our results are also of importance to the study of mass inflation and the stability of Cauchy horizons during a dynamical gravitational collapse of charged matter to form a charged black-hole