Collapse of self-interacting scalar field in anti-de Sitter space

TL;DR

This paper studies how a self-interaction term in a scalar field affects gravitational collapse in anti-de Sitter space, revealing that positive coupling suppresses black hole formation while negative enhances it, with universal scaling near criticality.

Contribution

It introduces a numerical analysis of self-interaction effects on scalar field collapse in AdS space, identifying universal scaling laws and susceptibilities.

Findings

Positive self-interaction suppresses black hole formation

Negative self-interaction enhances collapse

Critical exponent for formation time is approximately 0.74

Abstract

The gravitational collapse of a massless scalar field with a self-interaction term $\lambda\phi^4$ in anti-de Sitter space is investigated. We numerically investigate the effect of the self-interaction term on the critical amplitudes, forming time of apparent horizon, stable island and energy transformation. The results show that a positive $\lambda$ suppresses the formation of black hole, while a negative $\lambda$ enhances the process. We define two susceptibilities to characterize the effect of the self-interaction on the black hole formation, and find that near the critical amplitude, there exists a universal scaling relation with the critical exponent $\alpha \approx 0.74$ for the time of black hole formation.