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*)?, where p labels a family of initial data, p* is the value of p at the threshold, and the critical exponent ? 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 L?, we find the oscillating behavior L??Re[(A?+iB?)(p-p*)?+i?]. The assumptions of the calculation hold for p=?/3 perfect fluid matter, and we calculate ??0.799 and ??0.231.