The singularity in supercritical collapse of a spherical scalar field

TL;DR

This paper investigates the nature of singularities formed during supercritical collapse of a spherical scalar field, combining analytical modeling with numerical simulations to reveal their structure and behavior.

Contribution

It provides a new analytical solution describing a monotonic, strong spacelike singularity in scalar field collapse and validates it with detailed numerical simulations.

Findings

Singularity is monotonic, scalar polynomial, and strong.

At late times, the singularity resembles Schwarzschild, with localized deviations.

Numerical results confirm the analytical predictions.

Abstract

We study the singularity created in the supercritical collapse of a spherical massless scalar field. We first model the geometry and the scalar field to be homogeneous, and find a generic solution (in terms of a formal series expansion) describing a spacelike singularity which is monotonic, scalar polynomial and strong. We confront the predictions of this analytical model with the pointwise behavior of fully-nonlinear and inhomogeneous numerical simulations, and find full compliance. We also study the phenomenology of the spatial structure of the singularity numerically. At asymptotically late advanced time the singularity approaches the Schwarzschild singularity, in addition to discrete points at finite advanced times, where the singularity is Schwarzschild-like. At other points the singularity is different from Schwarzschild due to the nonlinear scalar field.