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, 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.

10 pages, 8 figures

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• Critical Collapse of Scalar Fields Beyond Axisymmetry
• Extreme $\ell$-boson stars
• Traversable $\ell$-wormholes supported by ghost scalar fields
• On the linear stability of $\ell$-boson stars with respect to radial perturbations
• Scalar field confinement as a model for accreting systems
• On the radial linear stability of nonrelativistic $\ell$-boson stars
• Einstein-Dirac system in semiclassical gravity
• Late-time tails of wave maps coupled to gravity
• Self Similar Collapse and the Raychaudhuri equation
• A Numerical Study of Boson Star Binaries
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• Dynamics of Nonlinear Waves on Bounded Domains
• Twist and higher modes of a complex scalar field at the threshold of collapse
• Noble gravitational atoms: Self-gravitating black hole scalar wigs with angular momentum number