Effects of magnetic field on the runaway instability of relativistic accretion tori near a rotating black hole

Runaway instability operates in accretion tori around black holes, where it affects systems close to the critical (cusp overflowing) configuration. The runaway effect depends on the radial profile l(R) of the angular momentum distribution of the fluid, on the dimension-less spin a of the central black hole (|a| ≤ 1), and other factors, such as self-gravity. Here we discuss the role of runaway instability within a framework of an axially symmetric model of perfect fluid endowed with a purely toroidal magnetic field.