  We present results from the first fully relativistic simulations of the
critical collapse of rotating radiation fluids. We observe critical scaling
both in subcritical evolutions, in which case the fluid disperses to infinity
and leaves behind flat space, and in supercritical evolutions that lead to the
formation of black holes. We measure the mass and angular momentum of these
black holes, and find that both show critical scaling with critical exponents
that are consistent with perturbative results. The critical exponents are
universal; they are not affected by angular momentum, and are independent of
the direction in which the critical curve, which separates subcritical from
supercritical evolutions in our two-dimensional parameter space, is crossed. In
particular, these findings suggest that the angular momentum decreases more
rapidly than the square of the mass, so that, as criticality is approached, the
collapse leads to the formation of a non-spinning black hole. We also
demonstrate excellent agreement of our numerical data with new closed-form
extensions of power-law scalings that describe the mass and angular momentum of
rotating black holes formed close to criticality.
