Twist-free axisymmetric critical collapse of a complex scalar field

TL;DR

This paper investigates the critical collapse of a complex scalar field in axisymmetric spacetimes, revealing how universality breaks down with increasing asphericity and providing insights into gravitational wave-driven collapse.

Contribution

It demonstrates the behavior of complex scalar field collapse near the critical threshold in axisymmetry, extending understanding beyond spherical symmetry and analyzing the role of gravitational waves.

Findings

Spherical critical solution matches Choptuik's solution.

Power-law exponents and periods vary with asphericity.

Collapse bifurcates away from the origin at high asphericity.

Abstract

Critical phenomena in gravitational collapse are characterized by the emergence of surprising structure in solution space, namely the appearance of universal power-laws and periodicities near the threshold of collapse, and a universal discretely self-similar solution at the threshold itself. The seminal work of M. Choptuik spurred a comprehensive investigation of extreme spherical spacetimes in numerical relativity, with analogous results for numerous matter models. Recent research suggests that the generalization to less symmetric scenarios is subtle. In twist-free axisymmetric vacuum collapse for instance, numerical evidence suggests a breakdown of universality of solutions at the threshold of collapse. In this study, we explore gravitational collapse involving a massless complex scalar field minimally coupled to general relativity. We employ the pseudospectral code BAMPS to investigate a neighborhood of the spherically symmetric critical solution in phase space, focusing on aspherical departures from it. First, working in explicit spherical symmetry, we find strong evidence that the spacetime metric of the spherical critical solution of the complex scalar field agrees with that of the Choptuik solution. We then examine universality of the behavior of solutions near the threshold of collapse as the departure from spherical symmetry increases, comparing with recent investigations of the real scalar field. We present a series of well-tuned numerical results and document shifts of the power-law exponent and periods as a function of the degree of asphericity of the initial data. At sufficiently high asphericities we find that the center of collapse bifurcates, on the symmetry axis, but away from the origin. Finally we look for and evaluate evidence that in the highly aspherical setting the collapse is driven by gravitational waves.