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arxiv 2406.03371 v2 pith:QI4EZXE2 submitted 2024-06-05 gr-qc astro-ph.HEhep-th

Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to S2 star orbit

classification gr-qc astro-ph.HEhep-th
keywords magneticstardipoleorbitsaroundblackellipticexternal
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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This study provides a comprehensive analytical investigation of the bound and unbound motion of magnetized particles orbiting a Schwarzschild black hole immersed in an external asymptotically uniform magnetic field, which includes all conceivable types of bounded and unbounded orbits. In particular, for planetary orbits, we perform a comparative analysis of our findings with the observed position of the S2 star carrying magnetic dipole moment around Sagittarius A* (Sgr A*). We found maximum and minimum values for the parameter of magnetic interaction between the magnetic dipole of the star and the external magnetic field, as well as the energy and angular momentum of the S2 star. As a result, we obtain estimations of the magnetic dipole of the star in order of $10^6 \rm \ G\cdot cm^{3}$. Additionally, we explore deflecting trajectories akin to gravitational Rutherford scattering. In obtaining the solutions for the orbital equations, we articulate the elliptic integrals and Jacobi elliptic functions, and our study is augmented by illustrative figures and simulations.

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    A magnetized Schwarzschild background shifts EMRI orbital dynamics and GW waveforms, with B~10^9 G producing ~1.3 rad dephasing over one year for a 10^6 M_sun system.