Collapse of Self-Interacting Scalar Field in Anti-de Sitter Space

摘要: 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 A suppresses the formation of black hole, while a negative A 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 approximate to 0.74 for the time of black hole formation.