Paradoxes of magnetorotational instability and their geometrical resolution

The magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs. By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI that appear in the limits of infinite and vanishing magnetic Prandtl number. For the latter case we derive a new strict limit of the critical Rossby number. This new limit of ${\rm Ro_c}=-0.802$,whichappearsforafiniteLundquistnumberof${\rm Lu}=0.618$, extends the formerly known inductionless Liu limit of $\mathrm{R}{\mathrm{o}}_{\mathrm{c}}=-0.828$ valid at $\mathrm{L}\mathrm{u}=0$.