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

The gravitational collapse of a massless scalar field with a self-interaction term $λϕ^4$ 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 $λ$ 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 $α\approx 0.74$ for the time of black hole formation.