Critical Collapse of massless scalar fields in asymptotically anti-de Sitter spacetime

Abstract We conduct numerical investigations on the critical collapse of spherically symmetric massless scalar fields in asymptotically anti-de Sitter spacetime. Our primary focus is on the behavior of the critical amplitude under various initial configurations of the scalar field. Through our numerical results, we obtain a formula that determines the critical amplitude $A^{*}$ in terms of the cosmological constant $\Lambda$: $A^{*}\propto (0.01360 \sigma/v_{0}+ 0.001751)\Lambda$, where $\sigma$ denotes the initial width of the scalar field, and $v_{0}$ is the initial position of the scalar field. Notably, we highlight that the slope of this linear relationship depends on the initial configuration of the scalar field.