Charged fluid tori with an approximate magnetic self-field around magnetized Schwarzschild black holes: A semi-analytic approach
Abstract
We study toroidal structures formed by a charged, non-self-gravitating perfect fluid orbiting a Schwarzschild black hole immersed in a poloidal magnetic field. To obtain analytic and semi-analytic solutions, we assume a cold, rest-mass-dominated fluid with uniform specific charge and zero conductivity, so the current is purely convective. This regime is formally opposite to the ideal GRMHD limit. The total magnetic field comprises a prescribed asymptotically uniform external component and an approximate self-field associated with the azimuthal current in the torus. We represent the latter by a regularized dipole approximation to the field of an effective circular current loop. Neglecting the self-field, the method of characteristics yields a general implicit solution of the integrability condition for a function parametrizing the specific-angular-momentum profile. A separately obtained cylindrically dependent class recovers a solution from our earlier work. For the radially dependent class, we integrate the Euler equations, obtain the enthalpy potential, and derive local conditions for equatorially centered tori. We then examine the field-free limit, both magnetic components separately, and their superposition. The external field supports closed tori within analytically derived parameter bounds, whereas no such equilibrium is found for the isolated approximate self-field within the numerically explored domain. In a representative combined-field sequence, the radial extent varies nonmonotonically with relative self-field strength: it increases for weak self-fields and decreases as the self-field becomes comparable to the external field. The results show how an approximate magnetic self-field modifies the morphology and domain of existence of charged-fluid tori.
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BibTeX
@misc{tlemissov2026charged,
title = {{Charged fluid tori with an approximate magnetic self-field around magnetized Schwarzschild black holes: A semi-analytic approach}},
author = {Abylaikhan Tlemissov and Jiri Kovar},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31577},
eprint = {2610.31577},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31577},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Charged fluid tori with an approximate magnetic self-field around magnetized Schwarzschild black holes: A semi-analytic approach
AU - Abylaikhan Tlemissov
AU - Jiri Kovar
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31577
UR - https://arxiv.org/abs/2610.31577
AB - We study toroidal structures formed by a charged, non-self-gravitating perfect fluid orbiting a Schwarzschild black hole immersed in a poloidal magnetic field. To obtain analytic and semi-analytic solutions, we assume a cold, rest-mass-dominated fluid with uniform specific charge and zero conductivity, so the current is purely convective. This regime is formally opposite to the ideal GRMHD limit. The total magnetic field comprises a prescribed asymptotically uniform external component and an approximate self-field associated with the azimuthal current in the torus. We represent the latter by a regularized dipole approximation to the field of an effective circular current loop. Neglecting the self-field, the method of characteristics yields a general implicit solution of the integrability condition for a function parametrizing the specific-angular-momentum profile. A separately obtained cylindrically dependent class recovers a solution from our earlier work. For the radially dependent class, we integrate the Euler equations, obtain the enthalpy potential, and derive local conditions for equatorially centered tori. We then examine the field-free limit, both magnetic components separately, and their superposition. The external field supports closed tori within analytically derived parameter bounds, whereas no such equilibrium is found for the isolated approximate self-field within the numerically explored domain. In a representative combined-field sequence, the radial extent varies nonmonotonically with relative self-field strength: it increases for weak self-fields and decreases as the self-field becomes comparable to the external field. The results show how an approximate magnetic self-field modifies the morphology and domain of existence of charged-fluid tori.
ER -