Free evolution of nonlinear scalar field collapse in double-null coordinates

TL;DR

This paper presents a numerical study of nonlinear scalar field collapse in spherical symmetry using double-null coordinates, revealing late-time inverse power-law tails consistent with linear theory predictions, for both neutral and charged black holes.

Contribution

It introduces a stable, second-order accurate numerical code for fully nonlinear scalar field collapse in double-null coordinates and analyzes late-time decay behaviors in various regions.

Findings

Decay of quasi-normal modes followed by inverse power-law tails.

Power indices match linearized theory predictions.

Similar tail behavior observed in charged black hole perturbations.

Abstract

We study numerically the fully nonlinear spherically-symmetric collapse of a self-gravitating, minimally-coupled, massless scalar field. Our numerical code is based on double-null coordinates and on free evolution of the metric functions and the scalar field. The numerical code is stable and second-order accurate. We use this code to study the late-time asymptotic behavior at fixed $r$ (outside the black hole), along the event horizon, and along future null infinity. In all three asymptotic regions we find that, after the decay of the quasi-normal modes, the perturbations are dominated by inverse power-law tails. The corresponding power indices agree with the integer values predicted by linearized theory. We also study the case of a charged black hole nonlinearly perturbed by a (neutral) self-gravitating scalar field, and find the same type of behavior---i.e., quasi-normal modes followed by inverse power-law tails, with the same indices as in the uncharged case.