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

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, Δl, decreases as l increases in such a way that the critical solution appears to become periodic in the limit. The mass-scaling exponent, γl, also decreases with l.