Charge scaling and universality in critical collapse

TL;DR

This paper investigates how charge affects critical gravitational collapse, predicting universal scaling laws for black hole mass and charge in charged scalar fields, extending previous zero-charge results.

Contribution

It introduces the first analysis of charge effects in critical collapse, predicting specific scaling exponents for mass and charge, and proposes universality classes based on charge parameters.

Findings

Black hole mass scales as (p - p*)^gamma with gamma ≈ 0.374.

Black hole charge scales as (p - p*)^delta with delta ≈ 0.883.

Charge influences the universality classes in critical collapse phenomena.

Abstract

Consider any 1-parameter family of initial data such that data with parameter value p > p* form black holes, and data with p < p* do not. As p -> p* from above ("critical collapse"), the black hole mass scales as M ~ (p-p*)^gamma, where the critical exponent gamma is the same for all such families of initial data. So far critical collapse has been investigated only for initial data with zero charge and zero angular momentum. Here we allow for U(1) charge. In scalar electrodynamics coupled to gravity, with action R + |(d + iqA) phi|^2 + F^2, we consider initial data with spherical symmetry and nonvanishing charge. From dimensional analysis and a previous calculation of Lyapunov exponents, we predict that in critical collapse the black hole mass scales as M ~ (p-p*)^gamma, and the black hole charge as Q ~ (p-p*)^delta, with gamma = 0.374 +- 0.001 (as for the real scalar field), and delta = 0.883 +- 0.007. We conjecture that, where there is no mass gap, this behavior generalizes to other charged matter models, with delta \ge 2 gamma. We suggest the existence of universality classes with respect to parameters such as q.