On Critical Exponents for Self-Similar Collapse

TL;DR

This paper systematically analyzes perturbations of self-similar solutions in the Einstein-axion-dilaton system, revealing how critical exponents vary with spacetime dimension, matter content, and solution types, using combined analytical and numerical methods.

Contribution

It introduces a comprehensive method to estimate Choptuik exponents across all conjugacy classes of $SL(2,R)$ and identifies how these exponents differ among various critical solutions.

Findings

Critical exponents depend on spacetime dimension and matter content.

Different types of critical solutions have distinct Choptuik exponents.

The methods apply to all three conjugacy classes of $SL(2,R)$ transformations.

Abstract

We explore systematically perturbations of self-similar solutions to the Einstein-axion-dilaton system, whose dynamics are invariant under spacetime dilations combined with internal $SL(2,R)$ transformations. The self-similar solutions capture the enticing behavior critical systems on the verge of gravitational collapse, in arbitrary spacetime dimensions. Our methods rest on a combination of analytical and numerical tools, apply to all three conjugacy classes of $SL(2,R)$ transformations and allow accurate estimates of the corresponding Choptuik exponents. It is well known that these exponents depend on the spacetime dimension and on the matter content. Our main result is that they also attain different values, even within a given conjugacy class, for the distinct types of critical solutions that we recently identified in the Einstein-axion-dilaton system.