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

Abstract

The gravitational collapse of a massless scalar field with a self-interaction term $\lambda {\varphi }^4$ 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.

7 pages, 5 figures

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• Critical phenomena in gravitational collapse of Husain-Martinez-Nunez scalar field
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