Critical Collapse of a Complex Scalar Field with Angular Momentum

TL;DR

This paper discovers a new non-spherical, discretely self-similar critical solution in axisymmetric gravitational collapse of a complex scalar field with angular momentum, revealing universal features within a specific symmetry class.

Contribution

It introduces a novel critical solution with angular momentum in scalar field collapse, characterized by specific self-similarity and scaling properties.

Findings

Critical solution is discretely self-similar with echoing exponent ~0.42.

Scaling exponent near criticality is approximately 0.11.

Solution appears universal within the symmetry class, up to a phase constant.

Abstract

We report a new critical solution found at the threshold of axisymmetric gravitational collapse of a complex scalar field with angular momentum. To carry angular momentum the scalar field cannot be axisymmetric; however, its azimuthal dependence is defined so that the resulting stress energy tensor and spacetime metric are axisymmetric. The critical solution found is non-spherical, discretely self-similar with an echoing exponent of 0.42 (+- 4%), and exhibits a scaling exponent of 0.11 (+- 10%) in near critical collapse. Our simulations suggest that the solution is universal (within the imposed symmetry class), modulo a family-dependent constant phase in the complex plane.