Emergence of Critical Phenomena from the Black Hole Interior
Phys. Rev. Lett. 137, 101401 – Published 1 September, 2026
DOI: https://doi.org/10.1103/b4bf-by6m
Abstract
The emergence of the 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 singularity emerges inside the black hole at the tip of the causal diamond. By varying the parameter of the initial profile for the scalar field toward the critical value , we observe the areal radius at the tip follows a power-law scaling, , with a universal critical exponent . 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 singularity inside spherically symmetric charged black holes, offering new insights into the nonlinear dynamics of strong gravitational fields.