Charged fluids encircling compact objects: force representations and conformal geometries

• Published in: Classical and quantum gravity 2020-12, Vol.37 (24), p.245007
• Main Authors: Kovář, Jiří, Kojima, Yasufumi, Slaný, Petr, Stuchlík, Zdeněk, Karas, Vladimír
• Format: Article
• Language: English
• Subjects: charged fluid toroidal structure; compact object; conformal geometry; electromagnetic field; force formalism; general relativity; gravitational field
• ISSN: 0264-9381; 1361-6382
• DOI: 10.1088/1361-6382/abbe70

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.