  Vorticity generation in accretion disks around Schwarzschild and Kerr black
holes is investigated in the context of magnetofluid dynamics derived for both
General Relativity (GR), and modified gravity formulations. In both cases, the
Kerr geometry leads to a "stronger" generation of vorticity than its
Schwarzschild counterpart. Of the two principal sources, the relativistic drive
peaks near the innermost stable circular orbit (isco), whereas the baroclinic
drive dominates at larger distances. Consequences of this new relativistic
vorticity source are discussed in several astrophysical settings.
