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 (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 (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.