Critical gravitational collapse with angular momentum: From critical exponents to scaling functions

We investigate the threshold of gravitational collapse with angular momentum, under the assumption that the critical solution is spherical and self-similar and has two growing modes, namely one spherical mode and one axial dipole mode (threefold degenerate). This assumption holds for perfect fluid matter with the equation of state $p=\kappa \rho$ if the constant $\kappa$ is in the range $0<\mathrm{}\kappa <1/9.\mathrm{}$ There is a region in the space of initial data where the mass and angular momentum of the black hole created in the collapse are given in terms of the initial data by two universal critical exponents and two universal functions of one argument. These expressions are similar to those for the correlation length and the magnetization in a ferromagnet near its critical point, as a function of the temperature and the external magnetic field. We discuss qualitative features of the scaling functions, and hence of critical collapse with high angular momentum.