Continuous Self-Similarity and $S$-Duality

TL;DR

This paper investigates the gravitational collapse of an axion/dilaton system, demonstrating that the critical solution exhibits continuous self-similarity and determining the associated mass scaling exponent through numerical and analytical methods.

Contribution

It provides the first numerical evidence of continuous self-similarity in axion/dilaton collapse and calculates the critical exponent for mass scaling.

Findings

Critical solution is continuously self-similar.

Critical exponent for mass scaling is approximately 0.264.

Numerical and analytical methods agree on the results.

Abstract

We study the spherically symmetric collapse of the axion/dilaton system coupled to gravity. We show numerically that the critical solution at the threshold of black hole formation is continuously self-similar. Numerical and analytical arguments both demonstrate that the mass scaling away from criticality has a critical exponent of $\gamma = 0.264$.