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 massless 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 $\ell$, and the system admits a well-known exact static solution. Working in polar coordinates, we first confirm that type II critical collapse occurs for a range of distinct initial configurations when $\ell =8$, 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 $\ell$, 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 ($\Delta \approx 3.4$) and critical exponent ($\gamma \approx 0.37$) remain essentially unchanged across all tested values of $\ell$.

8 pages, 3 figures