Higher Dimensional Choptuik Scaling in Painleve Gullstrand Coordinates

TL;DR

This paper studies how critical collapse behavior, specifically Choptuik scaling, extends to higher dimensions using Painleve-Gullstrand coordinates, confirming cusps in the scaling relationship and analyzing the critical exponent's asymptotic behavior.

Contribution

It demonstrates the presence of cusps in the periodic scaling in higher dimensions and explores the critical exponent's approach to 1/2 as dimensions increase.

Findings

Cusps in the periodic scaling relationship are confirmed in higher dimensions.

The critical exponent approaches 1/2 as the number of spacetime dimensions increases.

Results are consistent with earlier predictions about the asymptotic behavior of the critical exponent.

Abstract

We investigate Choptuik scaling in the spherically symmetric collapse of a massless scalar field in higher dimensions using Painleve-Gullstrand (P-G) coordinates. Our analysis confirms the presence in higher dimensions of the cusps in the periodic scaling relationship recently observed in four dimensional collapse. In addition, we address the issue of the asymptotic behaviour of the critical exponent as the number of spacetime dimensions gets large. Our results are consistent with earlier work suggesting that the critical exponent monotonically approaches 1/2 in this limit.