Universal Scaling and Echoing in Gravitational Collapse of a Complex Scalar Field

TL;DR

This paper investigates the universal scaling and echoing phenomena in the gravitational collapse of a complex scalar field, revealing new behaviors and properties of the endstate in a spherically symmetric, self-similar setting.

Contribution

It derives a new solution to Einstein-scalar equations demonstrating modified universal scaling and echoing in complex scalar collapse.

Findings

Universal scaling and echoing are observed with different characteristics.

Collapse results in an outgoing scalar radiation pulse with flat spacetime inside.

A new analytical solution describing the collapse dynamics is presented.

Abstract

This paper studies gravitational collapse of a complex scalar field at the threshold for black hole formation, assuming that the collapse is spherically symmetric and continuously self-similar. A new solution of the coupled Einstein-scalar field equations is derived, after a small amount of numerical work with ordinary differential equations. The universal scaling and echoing behavior discovered by Choptuik in spherically symmetrical gravitational collapse appear in a somewhat different form. Properties of the endstate of the collapse are derived: The collapse leaves behind an irregular outgoing pulse of scalar radiation, with exactly flat spacetime within it.