Collapse of Self-Interacting Scalar Field in Anti-de Sitter Space**Supported by the National Natural Science Foundation of China under Grant Nos. 11375247 and 11435006

Abstract

The gravitational collapse of a massless scalar field with a self-interaction term λφ4 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 λ suppresses the formation of black hole, while a negative λ 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 α ≈ 0.74 for the time of black hole formation.