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    Emergence of Critical Phenomena from the Black Hole Interior

    Caiying Shao1,*, Jun-Qi Guo2,†, Yu Tian1,‡, and Hongbao Zhang3,4,§

    • *Contact author: shaocaiying@ucas.ac.cn
    • †Contact author: sps_guojq@ujn.edu.cn
    • ‡Contact author: ytian@ucas.ac.cn
    • §Contact author: hongbaozhang@bnu.edu.cn

    Phys. Rev. Lett. 137, 101401 – Published 1 September, 2026

    DOI: https://doi.org/10.1103/b4bf-by6m

    Abstract

    The emergence of the r=0 singularity inside a spherically symmetric charged black hole is studied numerically within the Einstein-Maxwell-real scalar model. When the scalar field reaches a critical strength, the r=0 singularity emerges inside the black hole at the tip of the causal diamond. By varying the parameter p of the initial profile for the scalar field toward the critical value p*, we observe the areal radius at the tip follows a power-law scaling, rS∝|p−p*|γ, with a universal critical exponent γ≈0.5. This remarkable discovery, analogous to Choptuik’s critical phenomena for the black hole formation, provides the first evidence of the universality and scaling for the emergence of the r=0 singularity inside spherically symmetric charged black holes, offering new insights into the nonlinear dynamics of strong gravitational fields.

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