  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.
