Angular momentum near the black hole threshold in scalar field collapse

TL;DR

This paper investigates how angular momentum behaves near the black hole formation threshold in scalar field collapse, using perturbation theory and numerical analysis to determine a critical exponent and observe fine structure in the scaling law.

Contribution

It introduces a second-order perturbative calculation of the black hole angular momentum critical exponent and combines it with previous numerical results for improved accuracy.

Findings

Critical exponent mu approximately 0.76

Identification of a quasi-periodic fine structure in the scaling law

Validation of second-order perturbation theory in this context

Abstract

For the formation of a black hole in the gravitational collapse of a massless scalar field, we calculate a critical exponent that governs the black hole angular momentum for slightly non-spherical initial data near the black hole threshold. We calculate the scaling law by second-order perturbation theory. We then use the numerical results of a previous first-order perturbative analysis to obtain the numerical value mu ~ 0.76 for the angular momentum critical exponent. A quasi-periodic fine structure is superimposed on the overall power law.