Critical behavior in the gravitational collapse of a scalar field with angular momentum in spherical symmetry

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, ${\ensuremath{\Delta}}_{l}$, decreases as $l$ increases in such a way that the critical solution appears to become periodic in the limit. The mass-scaling exponent, ${\ensuremath{\gamma}}_{l}$, also decreases with $l$.