Gravitomagnetic Vorticity Generation in Accretion Disk: Implications for Plasma Flow Stability in the Weak-Field Limit

We explore vorticity generation in accretion disks around slowly rotating black holes within the weak-field, low-velocity limit of general relativity. Our analysis highlights the role of the gravitomagnetic field, induced by black hole rotation, as a novel source of vorticity (both magnetic field and flow vortex) in plasmas with non-negligible vertical structure. We derive the vorticity generation rate, which vanishes at the disc’s mid-plane but increases with vertical height, potentially influencing plasma flow stability. Additionally, we calculate the enstrophy density generation rate as a measure of turbulence and dissipation, observing its growth away from the mid-plane. While our weak-field approximation limits precise conclusions near the innermost stable circular orbit, our findings suggest that gravitomagnetic effects may constrain the vertical structure of accretion discs, particularly in tenuous disks around low-mass, rapidly rotating black holes. This work offers new insights into the interplay between relativistic frame-dragging and plasma dynamics.