Angular momentum at the black hole threshold

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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 γis 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 L we find the oscillating behavior L ≃ Re[(A + i B) (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.