  Strong magnetic fields in relativistic stars can be a cause of crust
fracturing, resulting in the excitation of global torsional oscillations. Such
oscillations could become observable in gravitational waves or in high-energy
radiation, thus becoming a tool for probing the equation of state of
relativistic stars. As the eigenfrequency of torsional oscillation modes is
affected by the presence of a strong magnetic field, we study torsional modes
in magnetized relativistic stars. We derive the linearized perturbation
equations that govern torsional oscillations coupled to the oscillations of a
magnetic field, when variations in the metric are neglected (Cowling
approximation). The oscillations are described by a single two-dimensional wave
equation, which can be solved as a boundary value problem to obtain
eigenfrequencies. We find that in the non-magnetized case, typical oscillation
periods of the fundamental l=2 torsional modes can be nearly a factor of two
larger for relativistic stars than previously computed in the Newtonian limit.
For magnetized stars, we show that the influence of the magnetic field is
highly dependent on the assumed magnetic field configuration and simple
estimates obtained previously in the literature cannot be used for identifying
normal modes observationally.
