On Choptuik's scaling in higher dimensions

TL;DR

This paper investigates Choptuik's critical gravitational collapse phenomenon in higher dimensions, extending previous findings and numerically analyzing universal scaling parameters across dimensions 4 to 11.

Contribution

It provides the first numerical analysis of Choptuik's scaling in dimensions 4 through 11, revealing how critical exponents vary with dimension.

Findings

Universal scaling exponent gamma and echoing period Delta are obtained for each dimension.

Gamma reaches a maximum and Delta a minimum around dimensions 11 to 13.

Results suggest a relation between critical collapse and black hole--black string systems.

Abstract

We extend Choptuik's scaling phenomenon found in general relativistic critical gravitational collapse of a massless scalar field to higher dimensions. We find that in the range 4 <= D <= 11 the behavior is qualitatively similar to that discovered by Choptuik. In each dimension we obtain numerically the universal numbers associated with the critical collapse: the scaling exponent gamma and the echoing period Delta. The behavior of these numbers with increasing dimension seems to indicate that gamma reaches a maximum and Delta a minimum value around 11 <= D <= 13. These results and their relation to the black hole--black string system are discussed.