Re-examining the stability of rotating horizonless black shells mimicking Kerr black holes

In arXiv:1705.10172 a string theory inspired alternative to gravitational collapse was proposed, consisting of a bubble of AdS space made up of ingredients from string theory. These ultra compact objects are $9/8$ times the size of the corresponding Schwarzschild black hole, but being within the photosphere are almost indistinguishable from them. Slowly rotating counterparts of these black shells were constructed in arXiv:1712.00511, which closely mimic a Kerr black hole, but have a quadrupole moment that differs from Kerr. Recently, arXiv:2109.09814 studied the dynamical stability of the stationary black shells against radial perturbations and accretion of matter, and examined a two parameter family of fluxes required for stability. In this paper, we re-examine the rotating black shells with particular attention to the constraints imposed by this dynamical analysis for non-rotating shells. Extrapolating these results to rotating shells, we find that they can indeed support themselves at a critical point in the gravitational potential. Additionally, requiring that they settle back to their new Buchdahl radius after accreting matter, uniquely fixes the fluxes required for dynamical stability. The flux parameters turn out to have an extremely simple form, and fulfil one of the constraints for perturbative radial stability while exactly saturating the other. The preferred quadrupole moment that we find, given some physical assumptions, is 7% less than Kerr.