Emergence of Critical Phenomena from the Black Hole Interior

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, r_{S}∝|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.