Choptuik scaling in null coordinates

TL;DR

This paper presents a numerical simulation of scalar field gravitational collapse using null coordinates, confirming Choptuik's critical phenomena and demonstrating a simple algorithm without adaptive mesh refinement.

Contribution

It introduces a straightforward null coordinate algorithm to verify Choptuik's critical phenomena in scalar field collapse.

Findings

Critical solution exhibits periodic self-similarity.

Verification of Choptuik's results using a simple algorithm.

No adaptive mesh refinement needed for the simulation.

Abstract

A numerical simulation is performed of the gravitational collapse of a spherically symmetric scalar field. The algorithm uses the null initial value formulation of the Einstein-scalar equations, but does {\it not} use adaptive mesh refinement. A study is made of the critical phenomena found by Choptuik in this system. In particular it is verified that the critical solution exhibits periodic self-similarity. This work thus provides a simple algorithm that gives verification of the Choptuik results.