  We consider black holes generically sourced by quantum matter described by
regular wavefunctions. This allows for integrable effective energy densities
and the removal of Cauchy horizons in spherically symmetric configurations.
Moreover, we identify the ultrarigid rotation of the Kerr spacetime as causing
the existence of an inner horizon in rotating systems, and describe general
properties for quantum matter cores at the centre of rotating black holes with
integrable singularities and no Cauchy horizon.
