Emergence of critical phenomena from the black hole interior

TL;DR

This paper demonstrates that the formation of the $r=0$ singularity inside charged black holes exhibits universal critical phenomena, with a power-law scaling and a critical exponent around 0.5, revealing new insights into black hole interior dynamics.

Contribution

It provides the first evidence of universality and scaling laws for the emergence of the $r=0$ singularity inside black holes, analogous to critical phenomena in gravitational collapse.

Findings

The $r=0$ singularity appears at a critical scalar field strength.

The areal radius at the singularity follows a power law near criticality.

The critical exponent is approximately 0.5, indicating universality.

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 of the black hole at the tip of the causal diamond. By varying the parameter $p$ of the initial profile for the scalar field towards the critical value ${p_*}$, we observe the areal radius at the tip follows a power law scaling, ${r_S } \propto {| {p - {p_*}}|^\gamma }$, with a universal critical exponent $\gamma\approx 0.5$. 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 black holes, offering new insights into the nonlinear dynamics of strong gravitational field.