Late-Time Tails in Gravitational Collapse of a Self-Interacting (Massive) Scalar-Field and Decay of a Self-Interacting Scalar Hair

TL;DR

This paper analytically and numerically investigates the decay behavior of self-interacting scalar fields around charged black holes, revealing that the decay tail is oscillatory and slower than any power-law at late times.

Contribution

It provides a detailed analytical and numerical analysis of the decay of self-interacting scalar hair in Reissner-Nordström spacetime, highlighting the unique late-time decay behavior.

Findings

Intermediate asymptotic tail is oscillatory and follows an inverse power-law decay.

Late-time decay of scalar hair is slower than any power-law.

Numerical simulations confirm analytical predictions.

Abstract

We study analytically the initial value problem for a self-interacting (massive) scalar-field on a Reissner-Nordstr\"om spacetime. Following the no-hair theorem we examine the dynamical physical mechanism by which the self-interacting (SI) hair decays. We show that the intermediate asymptotic behaviour of SI perturbations is dominated by an oscillatory inverse power-law decaying tail. We show that at late-times the decay of a SI hair is slower than any power-law. We confirm our analytical results by numerical simulations.