Magnetofluid dynamics in curved spacetime : theory and application
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A grand unified field tensor [Greek capital letter Mu] [Greek small letter mu] [Greek small letter nu] is constructed from Maxwell's field tensor and appropriately modified flow field, both nonminimally coupled to gravity, to analyze the dynamics of hot charged fluids in curved background space-time. With suitable 3+1 decomposition, this new formalism of hot fluid is then applied to investigate vorticity generation and a class of states known as the Beltrami-Bernoulli (BB) equilibria in the accretion disk around Schwarzschild and Kerr black holes. Of the two principle sources of vorticity i.e. baroclinic and relativistic, the relativistic drive peaks near innermost (isco) circular orbit for both black holes, whereas baroclinic drive dominates at larger distances. For General Relativity as well as modified gravity, the Kerr geometry leads to a ``stronger" vorticity generation than its Schwarzschild counterpart. On the other hand, modelling the disk plasma as a Hall MHD system, it has been shown that velocity/magnetic decay rate gets altered due to space time curvature, for example the velocity profile in BB states deviate substantially from the predicted geodesic velocity profiles. Moreover, these equilibrium states have their origin in the two helicity invariants which conspire to introduce a new oscillatory length scale into the system that is strongly influenced by relativistic and thermal effects. Consequences of this formalism are also discussed in several astrophysical settings.