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We study critical phenomena in the collapse of rotating ultrarelativisticperfect fluids, in which the pressure $P$ is related to the total energydensity $\rho$ by $P=\kappa\rho$, with $\kappa$ a constant. We generalizeearlier results for radiation fluids with $\kappa=1/3$ to other values of$\kappa$, focussing on $\kappa < 1/9$. For $1/9<\kappa \lesssim 0.49$, thecritical solution has only one unstable, growing mode, which is sphericallysymmetric. For supercritical data it controls the black hole mass, while forsubcritical data it controls the maximum density. For $\kappa<1/9$, anadditional axial $l=1$ mode becomes unstable. This controls either the blackhole angular momentum, or the maximum angular velocity. In theory, theadditional unstable $l=1$ mode changes the nature of the black hole thresholdcompletely: at sufficiently large initial rotation rates $\Omega$ andsufficient fine-tuning of the initial data to the black hole threshold weexpect to observe nontrivial universal scaling functions (familiar fromcritical phase transitions in thermodynamics) governing the black hole mass andangular momentum, and, with further fine-tuning, eventually a finite black holemass almost everywhere on the threshold. In practice, however, the secondunstable mode grows so slowly that we do not observe this breakdown of scalingat the level of fine-tuning we can achieve, nor systematic deviations from theleading-order power-law scalings of the black hole mass. We do see systematiceffects in the black-hole angular momentum, but it is not clear yet if theseare due to the predicted non-trivial scaling functions, or to nonlinear effectsat sufficiently large initial angular momentum (which we do not account for inour theoretical model).

Critical gravitational collapse with angular momentum II: soft equations of state