Angular momentum near the black hole threshold in scalar field collapse

For the formation of a black hole in the gravitational collapse of a massless scalar field, we calculate a critical exponent that governs the black hole angular momentum for slightly non-spherical initial data near the black hole threshold. We calculate the scaling law by second-order perturbation theory. We then use the numerical results of a previous first-order perturbative analysis to obtain the numerical value $\mu \simeq 0.76$ for the angular momentum critical exponent. A quasi-periodic fine structure is superimposed on the overall power law.