Angular momentum at the black hole threshold

Near the black hole threshold in phase space, the black hole mass as a function of the initial data shows the “critical scaling” M≃C(p-p_*)^γ, where p labels a family of initial data, p_* is the value of p at the threshold, and the critical exponent γ is universal for a given matter model. The black hole charge Q obeys a similar law. To complete the picture, we include the angular momentum as a perturbation. For the black hole angular momentum L⃗, we find the oscillating behavior L⃗≃Re[(A⃗+iB⃗)(p-p_*)^μ+iω]. The assumptions of the calculation hold for p=ρ/3 perfect fluid matter, and we calculate μ≃0.799 and ω≃0.231.