Critical phenomena in gravitational collapse with two competing massless matter fields

Abstract

In the gravitational collapse of matter beyond spherical symmetry, gravitational waves are necessarily present. On the other hand, gravitational waves can collapse to a black hole even without matter. One might therefore wonder whether the interaction and competition between the matter fields and gravitational waves affects critical phenomena at the threshold of black hole formation. As a toy model for this, we study type II critical collapse with two matter fields in spherical symmetry, namely a scalar field and a Yang-Mills field. On their own, both display discrete self-similarity (DSS) in type II critical collapse, and we can take either one of them as a toy model for gravitational waves. To our surprise, in numerical time evolutions we find that, for sufficiently good fine-tuning, the scalar field always dominates on sufficiently small scales. We explain our results by the conjectured existence of a "quasi-discretely self-similar" (QSS) solution shared by the two fields, equal to the known Yang-Mills critical solution at infinitely large scales and the known scalar field critical solution (the Choptuik solution) at infinitely small scales, with a gradual transition from one field to the other. This QSS solution itself has only one unstable mode, and so acts as the critical solution for any mixture of scalar field and Yang-Mills initial data.

Section on the numerical method expanded

References in corpus (10)

• On critical collapse of gravitational waves
• Evolutions of centered Brill waves with a pseudospectral method
• Aspherical deformations of the Choptuik spacetime
• Multi-oscillating Boson Stars
• Critical behavior in 3-d gravitational collapse of massless scalar fields
• Critical gravitational collapse with angular momentum II: soft equations of state
• Critical gravitational collapse with angular momentum
• Critical collapse of ultra-relativistic fluids: damping or growth of aspherical deformations
• Critical phenomena in the general spherically symmetric Einstein-Yang-Mills system
• Type II critical behavior of gravitating magnetic monopoles

Cited by in corpus (12)

• Evolution of Brill waves with an adaptive pseudospectral method
• Gauge structure of the Einstein field equations in Bondi-like coordinates
• Critical phenomena in the gravitational collapse of electromagnetic dipole and quadrupole waves
• Twist-free axisymmetric critical collapse of a complex scalar field
• Simulations of gravitational collapse in null coordinates: II. Critical collapse of an axisymmetric scalar field
• Numerical convergence of model Cauchy-characteristic extraction and matching
• Are gravitating magnetic monopoles stable?
• Simulations of gravitational collapse in null coordinates: I. Formulation and weak-field tests in generalised Bondi gauges
• Investigation into Length Scale Dominance in Critical Black Hole Formation
• Critical phenomena in gravitational collapse with competing scalar field and gravitational waves, in 4+1 dimensions
• Boundary dynamics in competing critical black hole formation
• A Nonlinear Endpoint of Charged Horizon Instabilities