Charged fluids encircling compact objects: force representations and conformal geometries

Abstract

Charged fluids rotating around compact objects can form unique equilibrium structures when ambient large-scale electromagnetic fields combine with strong gravity. Equatorial as well as off-equatorial toroidal structures are among such figures of equilibrium with a direct relevance for astrophysics. To investigate their geometrical shapes and physical properties in the near-horizon regime, where effects of general relativity play a significant role, we commonly employ a scheme based on the energy-momentum conservation written in a standard representation. Here, we develop its interesting alternatives in terms of two covariant force representations, both based on a hypersurface projection of the energy-momentum conservation. In a proper hypersurface, space-like forces can be defined, following from a decomposition of the fluid four-acceleration. Each of the representations provides us with an insight into properties of the fluid flow, being well reflected in related conformal hypersurface geometries; we find behaviour of centrifugal forces directly related to geodesics of these conformal hypersurfaces and their embedding diagrams. We also reveal correspondence between the charged fluid flow world-lines from an ordinary spacetime, and world-lines determined by a charged test particles equation of motion in a conformal spacetime.

Charged fluid structures around a rotating compact object with a magnetic dipole field

“…Equilibrium configurations of a rotating fluid and the conditions for their stability play an important role in astrophysics [1,2]. Previously, we discussed a special case of electrically charged, non-conductive, energetically bound figures of fluid equilibria around black holes [3][4][5][6][7][8][9]. A possibility of (even small) non-vanishing electrical charge greatly enlarges the parameter space of the system.…”