10 56]). Notice that even though we do not impose any type of symmetry, no asymmetric, unstable modes are observed. This behavior is consistent with previous work which studied the possible onset of axisymmetric insta- bilities [57]. These previous studies found that such in- stabilities require high rotation rates characterized by T/W > 0 . 25 in contrast to those studied here for which T/W ≤ 0 . 1. Consequently, we see no evidence for defor- mations of the star as would be apparent by monitoring the distortion parameters moving away from zero. In Fig. 5, we show an example of such an evolution at three successively finer resolutions. Because the star is collapsing, the maximum density increases dramatically. The magnetic field remains essentially poloidal through- out the collapse and its maximum magnitude increases due to the resulting compression of the field lines. De- spite this increase, the magnetic field plays no important role in the collapse since its associated pressure is still several orders of magnitude smaller than the fluid pres- sure. While we do observe an increase in the norm of the divergence, the growth is not particularly fast and the divergence remains small in absolute terms and relative to the magnetic field. Fig. 6 displays two snapshots of the density and mag- netic field strength of the collapsing star tested in Fig. 5. The first one illustrates a stage during the collapse before an apparent horizon forms. The second one shows the behavior after an apparent horizon is found and its inte- rior excised. The apparent horizon appears at t ≃ 0 . 6 P , when the maximum of the density is ρ$_{max}$ = 0 . 271 and the minimum of the lapse is α$_{min}$ = 0 . 2. Previous work presented in [53] argues that, in general, unstable stars should either collapse to a black hole or ex- pand and oscillate about a stable stellar solution. Seeking to duplicate this behavior, we perturb an unstable star. Indeed, as shown in Fig. 7, we find precisely the behav- ior described. If our perturbation increases the pressure sufficiently, we find a star which expands and oscillates about some other, presumably stable solution. However, if we choose a perturbation which barely increases the pressure, the star collapses to a black hole. However, given the interest in black hole critical phe- nomena (see [58, 59]) over the past couple of decades, we study in detail the separation between these two be- haviors. That is, we continue to adjust A$_{p}$ in Eq. (53) searching for a value A ∗ p above which one finds black hole formation, and below which one finds an expanding so- lution (the way we have parameterized the pressure per- turbation, A ∗ p < 0). As apparent from Fig. 7, the more one continues this tuning, the longer the unstable star survives. This type of tuning is reminiscent of a similar analysis of an unstable, irregular static solution [60]. What these results suggest is that the unstable solution (i) sits at the threshold of black hole formation with (ii) a single unstable mode. That small perturbations about the solution send it ei- FIG. 7: The maximum density ρ max as a function of time for an unstable, perturbed ( m = 3 in Eq. (53)), non-magnetic, rotating star. The (unperturbed) initial star has central en- thalpy 0 . 8 and rotates at the mass shedding limit. Solutions resulting from tuning the amplitude of the perturbation A$_{p}$ to roughly one part in 10 6 show the two disparate outcomes (as discussed in [53]): collapse to black hole or violent oscillations about a stable stellar solution with equivalent mass. With more tuning, the star resembles the initial, unstable solution for a longer time. Perturbations of Unstable Stars FIG. 6: Density ρ 0 and magnetic field strength on the y = 0 plane for the same star as shown in Fig. 5. The density is shown with respect to the colormap while the contours denote the magnetic field, which is equally spaced from 0 to 5 × 10 $^{15}$G. The top left corresponds to t = 0 . 5 P while the the top right to t = 0 . 9 P (the circle shown represents the apparent horizon.) The bottom plot illustrates the normalized mass as a function of time, along with its rate of change.