Circular motion and fundamental frequencies of charged particles in dipole magnetic field around magnetized Bocharova--Bronnikov--Melnikov--Bekenstein black holes
Abstract
We examine the field produced by a stationary current loop encircling a static Bocharova--Bronnikov--Melnikov--Bekenstein (BBMB) black hole and the response of charged test particles. From the dipole projection of Maxwell's equations, we obtain closed-form interior and exterior radial functions, and we test them against a multipole expansion of the localized source whose radial functions are also elementary. Every horizon-regular mode vanishes at the degenerate horizon r+=M, so the magnetic flux through the horizon is zero. For a loop at r0=10M, the dipole errors in the equatorial potential and polar field remain below 10% for r≲0.42 r0 and r≳3.02 r0, but reach about 40% and 80% close to the loop. Using the resulting potential, we study the effective potential, circular orbits, the innermost stable circular orbit (ISCO), a binding-energy proxy, and epicyclic frequencies. Because the dipole field reverses its equatorial direction across the loop, a positive magnetic coupling ℬ acts oppositely on the two sides. Above ℬc≃0.0119, the prograde radially stable orbits split into two bands separated by an unstable gap. At ℬ=0.2, the ISCO moves from 4M to 2.97M, the exterior band begins at 45.46M, and the ISCO binding-energy proxy grows from 8.14% to 23.39%, compared with 5.72% for neutral particles around a Schwarzschild black hole. For negative coupling, exterior orbits can be radially stable but vertically unstable. Higher multipoles preserve the large-coupling trends but shift the near-loop values appreciably, so the near-loop results apply to the projected source rather than to a thin ring.
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BibTeX
@misc{abdurakhmonov2026circular,
title = {{Circular motion and fundamental frequencies of charged particles in dipole magnetic field around magnetized Bocharova--Bronnikov--Melnikov--Bekenstein black holes}},
author = {Ozodbek Abdurakhmonov and Mardon Abdullaev and Javlon Rayimbaev and Ilkhomjon Makhmudov and Saidmuhammad Ahmedov and Muhammad Matyoqubov},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07525},
eprint = {2611.07525},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07525},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Circular motion and fundamental frequencies of charged particles in dipole magnetic field around magnetized Bocharova--Bronnikov--Melnikov--Bekenstein black holes
AU - Ozodbek Abdurakhmonov
AU - Mardon Abdullaev
AU - Javlon Rayimbaev
AU - Ilkhomjon Makhmudov
AU - Saidmuhammad Ahmedov
AU - Muhammad Matyoqubov
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07525
UR - https://arxiv.org/abs/2611.07525
AB - We examine the field produced by a stationary current loop encircling a static Bocharova--Bronnikov--Melnikov--Bekenstein (BBMB) black hole and the response of charged test particles. From the dipole projection of Maxwell's equations, we obtain closed-form interior and exterior radial functions, and we test them against a multipole expansion of the localized source whose radial functions are also elementary. Every horizon-regular mode vanishes at the degenerate horizon r_+=M, so the magnetic flux through the horizon is zero. For a loop at r_0=10M, the dipole errors in the equatorial potential and polar field remain below 10% for r≲0.42 r_0 and r≳3.02 r_0, but reach about 40% and 80% close to the loop. Using the resulting potential, we study the effective potential, circular orbits, the innermost stable circular orbit (ISCO), a binding-energy proxy, and epicyclic frequencies. Because the dipole field reverses its equatorial direction across the loop, a positive magnetic coupling ℬ acts oppositely on the two sides. Above ℬ_c≃0.0119, the prograde radially stable orbits split into two bands separated by an unstable gap. At ℬ=0.2, the ISCO moves from 4M to 2.97M, the exterior band begins at 45.46M, and the ISCO binding-energy proxy grows from 8.14% to 23.39%, compared with 5.72% for neutral particles around a Schwarzschild black hole. For negative coupling, exterior orbits can be radially stable but vertically unstable. Higher multipoles preserve the large-coupling trends but shift the near-loop values appreciably, so the near-loop results apply to the projected source rather than to a thin ring.
ER -