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arXiv · 2606.03751

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

Li-Jie Xin·Xiangdong Zhang
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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 $\ell$.

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Li-Jie Xin, Xiangdong Zhang. 2026-06-02. Critical collapse of a self-interacting scalar field in asymptotically anti-de Sitter spacetime. https://arxiv.org/abs/2606.03751

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