Angular momentum at the black hole threshold

TL;DR

This paper investigates the behavior of angular momentum near the black hole formation threshold, revealing oscillatory scaling laws and calculating specific critical exponents for perfect fluid matter.

Contribution

It extends critical phenomena analysis to include angular momentum, deriving oscillatory scaling laws and computing critical exponents for perfect fluid models.

Findings

Angular momentum exhibits oscillatory scaling near the threshold.

Calculated critical exponents: μ ≈ 0.799, ω ≈ 0.231.

Results apply to p=ρ/3 perfect fluid matter.

Abstract

Near the black hole threshold in phase space, the black hole mass as a function of the initial data shows the "critical scaling" M \simeq C (p-p_*)^\gamma, where p labels a family of initial data, p_* is the value of p at the threshold, and the critical exponent \gamma is universal for a given matter model. The black hole charge Q obeys a similar law. To complete the picture, we include angular momentum as a perturbation. For the black hole angular momentum \vec L we find the oscillating behavior \vec L \simeq Re[ (\vec A + i \vec B) (p-p_*)^{\mu+i\omega} ]. The assumptions of the calculation hold for p = \rho / 3 perfect fluid matter, and we calculate \mu \simeq 0.799 and \omega \simeq 0.231.