A semi-linear wave model for critical collapse

Abstract

In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are self-similar and are, in a certain sense, unique. To an extent yet to be fully understood, the same phenomena persist beyond spherical symmetry. It is therefore desirable to construct models that exhibit such symmetry at the threshold of blow-up. Starting with deformations of the wave equation, we discuss models which have discretely self-similar threshold solutions. We study threshold solutions in the past light cone of the blow-up point. In spherical symmetry there is a sense in which a unique critical solution exists. Spherical numerical evolutions are also presented for more general models, and exhibit similar behavior. Away from spherical symmetry threshold solutions attain more freedom. Different topologies of blow-up are possible, and even locally the critical solution needs reinterpretation as a parameterized family.

arXiv comment18 pages, 9 figures

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• Critical phenomena in the gravitational collapse of electromagnetic dipole and quadrupole waves
• Twist-free axisymmetric critical collapse of a complex scalar field
• Simulating binary black hole mergers using discontinuous Galerkin methods
• Quantum correlations in a gravitational collapse simulation with SpheriCo.jl
• Comparison of linear Brill and Teukolsky waves