Mass gap in the critical gravitational collapse of a kink

TL;DR

This paper investigates the gravitational collapse of a kink in spherical symmetry, revealing a mass gap at the black hole formation threshold and analyzing the self-similar structure of the resulting spacetime.

Contribution

It provides the first detailed numerical analysis of the mass gap phenomenon in kink collapse and characterizes the self-similar structure of the spacetime.

Findings

Confirmation of a mass gap in black hole formation.

Identification of a universal mass scaling law with exponent ~0.37.

Observation of self-similar spacetime structure with period ~3.4.

Abstract

We study the gravitational collapse of a kink within spherical symmetry and the characteristic formulation of General Relativity. We explore some expected but elusive gravitational collapse issues which have not been studied before in detail, finding new features. The numerical one-parametric solution and the structure of the spacetime are calculated using finite differences, Galerkin collocation techniques, and some scripting for automated grid coverage. We study the threshold of black hole formation and confirm a mass gap in the phase transition. In the supercritical case we find a mass scaling power law $M_{BH}={M^*_{BH}}+K[\lambda-\lambda^*]^{2\gamma}+f(K[\lambda-\lambda^*]^{2\gamma})$, with $\gamma\approx 0.37$ independent of the initial data for the cases considered, and $M^*_{BH}$, $K$ and $\lambda^*$ each depending on the initial datum. The spacetime has a self-similar structure with a period of $\Delta\approx 3.4$. In the subcritical case the Bondi mass at null infinity decays in cascade with $\Delta/2$ interval as expected.