Comment on "linear instability of magnetic Taylor-Couette flow with Hall effect"

In the paper we comment on [Rudiger and Shalybkov (RS), Phys. Rev. E 69, 016303 (2004)], the instability of the Taylor-Couette flow interacting with a homogeneous background field subject to the Hall effect is studied. We correct a falsely generalizing interpretation of results presented there which could be taken to disprove the existence of the Hall-drift-induced magnetic instability described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103 (2002). It is shown that, in contrast to what is suggested by RS, no additional shear flow is necessary to enable such an instability with a nonpotential magnetic background field, whereas for a curl-free one it is. In the latter case, the instabilities found in RS in situations where neither a hydrodynamic nor a magnetorotational instability exists are demonstrated to be most likely magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are clarified.