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 critical amplitude in terms of cosmological constant Λ: , where σ denotes the initial width of the scalar field and 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.