Critical Behavior in the Gravitational Collapse of a Scalar Field with Angular Momentum in Spherical Symmetry

TL;DR

This paper investigates the critical gravitational collapse of a scalar field with angular momentum in spherical symmetry, revealing that critical solutions are discretely self-similar with properties changing with angular momentum.

Contribution

It introduces a novel approach to model angular momentum effects in scalar field collapse and analyzes how critical solutions depend on angular momentum quantum number l.

Findings

Critical solutions are discretely self-similar for various l values.

The self-similar period decreases as angular momentum increases.

The mass scaling exponent decreases with increasing angular momentum.

Abstract

We study the critical collapse of a massless scalar field with angular momentum in spherical symmetry. In order to mimic the effects of angular momentum we perform a sum of the stress-energy tensors for all the scalar fields with the same eigenvalue, l, of the angular momentum operator and calculate the equations of motion for the radial part of these scalar fields. We have found that the critical solutions for different values of l are discretely self-similar (as in the original l=0 case). The value of the discrete, self-similar period, Delta_l, decreases as l increases in such a way that the critical solution appears to become periodic in the limit. The mass scaling exponent, gamma_l, also decreases with l.