Critical Exponents and Stability at the Black Hole Threshold for a Complex Scalar Field

TL;DR

This study investigates the stability and critical behavior of a complex scalar field during gravitational collapse, calculating the critical exponent and identifying an unstable mode at the black hole formation threshold.

Contribution

It provides the first linear perturbation analysis of the complex scalar critical solution and determines the critical exponent and instability mode.

Findings

Critical exponent for black hole mass is approximately 0.387106.

The critical solution exhibits an unstable oscillatory mode.

The study confirms the instability of the critical solution.

Abstract

This paper continues a study on Choptuik scaling in gravitational collapse of a complex scalar field at the threshold for black hole formation. We perform a linear perturbation analysis of the previously derived complex critical solution, and calculate the critical exponent for black hole mass, $\gamma \approx 0.387106$. We also show that this critical solution is unstable via a growing oscillatory mode.