Paradoxes of magnetorotational instability and their geometrical resolution.

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 strict limit of the critical Rossby number. This limit of Ro(c)=-0.802, which appears for a finite Lundquist number of S=0.618, extends the formerly known inductionless Liu limit of Ro(c)=-0.828 valid at S=0.