Critical collapse of a self-interacting scalar field in asymptotically anti-de Sitter spacetime

Abstract We study the critical gravitational collapse of a spherically symmetric scalar field in asymptotically anti-de Sitter (AdS) spacetime. The scalar field potential adopted here is inversely proportional to the square of the AdS curvature radius $$\ell $$ ℓ , and the system admits a well-known exact static solution [1]. Working in polar coordinates, we first confirm that type II critical collapse occurs for a range of distinct initial configurations when $$\ell =8$$ ℓ = 8 , where the measured echoing period and critical exponent are in excellent agreement with Choptuik’s classic results. We then fine-tune the initial amplitude of the scalar field for a series of AdS radii $$\ell $$ ℓ , performing calculations in both polar coordinates and double null coordinates to cross-validate our results. We find that the form of the potential does not alter the critical behavior of gravitational collapse in any meaningful way: in particular, both the echoing period ( $$\Delta \approx 3.4$$ Δ ≈ 3.4 ) and critical exponent ( $$\gamma \approx 0.37$$ γ ≈ 0.37 ) remain essentially unchanged across all tested values of $$\ell $$ ℓ . We also analyze the evolution equation near the center during critical collapse, find that the cosmological term and scalar field potential term are negligible, and conclude that the spacetime near the center is approximately conformally flat.