Charged fluids encircling compact objects: force representations and conformal geometries

TL;DR

This paper explores the geometrical and physical properties of charged fluids around compact objects in strong gravitational fields, introducing new covariant force representations and analyzing their relation to conformal geometries and test particle motion.

Contribution

It develops alternative covariant force representations based on hypersurface projections, providing new insights into charged fluid dynamics near black holes in the context of conformal geometries.

Findings

Centrifugal forces relate to geodesics of conformal hypersurfaces.

New force representations reveal properties of charged fluid flow.

Correspondence established between fluid world-lines and test particle trajectories.

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.