Surveying the implications of generalized vortical dynamics in curved space-time

We present the extension of the magnetofluid vortical formalism to a general relativistic framework and demonstrate the versatility of the model in providing insight into astrophysical plasmas beyond the capabilities of most contemporary models. Specifically, we detail the construction of three tools for characterizing plasmas in curved space-time; (i) The unification of the flow vorticity with the magnetic field permits the derivation of a clear relationship between the two vorticities in curved space-time, particularly evident in pair plasmas; (ii) The simplified characterization of plasma states provided by the formalism facilitates a description and analysis of a broad class of equilibria, and we have here delineated the physically valid regime of these solutions around black holes, along with finding an explicit equation of state which ensures generalized helicity conservation; (iii) We explicitly extend to curved space-times the special relativistic incorporation of entropy into the magnetofluid vorticity, here constructing a grand generalized vorticity. The robust nature of this form promotes studies into both vorticity generation and evolution and additionally reveals a fundamental conserved helicity in the plasmas around compact objects.