Scale invariance and critical gravitational collapse

TL;DR

This paper investigates scale invariant formulations of the Choptuik critical solution, finding a new system that evolves periodically and could extend to more general gravitational collapse scenarios.

Contribution

It introduces a novel scale invariant variable system based on maximal slicing that exhibits periodic evolution in critical gravitational collapse.

Findings

The previously proposed scale invariant system does not evolve periodically.

The new system based on maximal slicing does evolve periodically.

Potential for generalization to axisymmetric or asymmetric cases.

Abstract

We examine ways to write the Choptuik critical solution as the evolution of scale invariant variables. It is shown that a system of scale invariant variables proposed by one of the authors does not evolve periodically in the Choptuik critical solution. We find a different system, based on maximal slicing. This system does evolve periodically, and may generalize to the case of axisymmetry or of no symmetry at all.