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Charged particle bound orbits around magnetized Schwarzschild black holes: S2 star and hotspot applications

Uktamjon Uktamov, Mohsen Fathi, Javlon Rayimbaev

Abstract

The dynamics of charged particles around magnetized black holes provide valuable insights into astrophysical processes near compact objects. In this work, we investigate the bound and unbound trajectories of charged particles in the vicinity of a Schwarzschild black hole immersed in an external, uniform magnetic field. By analyzing the effective potential and solving the corresponding equations of motion, we classify the possible orbital configurations and identify the critical parameters governing the transition between stable and escape trajectories. The influence of the magnetic field strength and particle charge on the orbital structure, energy, and angular momentum is systematically explored. Applications of the obtained results are discussed in the context of the S2 star orbiting Sagittarius A* and the motion of bright hotspots detected near the event horizon, offering a potential interpretation of recent observations in terms of magnetized dynamics. The study contributes to a deeper understanding of charged-particle motion around black holes and its relevance to high-energy astrophysical phenomena in the galactic center.

Charged particle bound orbits around magnetized Schwarzschild black holes: S2 star and hotspot applications

Abstract

The dynamics of charged particles around magnetized black holes provide valuable insights into astrophysical processes near compact objects. In this work, we investigate the bound and unbound trajectories of charged particles in the vicinity of a Schwarzschild black hole immersed in an external, uniform magnetic field. By analyzing the effective potential and solving the corresponding equations of motion, we classify the possible orbital configurations and identify the critical parameters governing the transition between stable and escape trajectories. The influence of the magnetic field strength and particle charge on the orbital structure, energy, and angular momentum is systematically explored. Applications of the obtained results are discussed in the context of the S2 star orbiting Sagittarius A* and the motion of bright hotspots detected near the event horizon, offering a potential interpretation of recent observations in terms of magnetized dynamics. The study contributes to a deeper understanding of charged-particle motion around black holes and its relevance to high-energy astrophysical phenomena in the galactic center.
Paper Structure (9 sections, 22 equations, 5 figures, 2 tables)

This paper contains 9 sections, 22 equations, 5 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Charged Particle Dynamics around SBHs in a Magnetic Field
  3. Equations of motion
  4. Circular orbits and stability
  5. Applications to hotspot orbits around Sgr A*
  6. Relativistic bound orbits and LP taxonomy
  7. Representative orbits
  8. Conclusions
  9. The coefficients in Eqs. \ref{['eq:angular']} and \ref{['eq:energy']}

Figures (5)

  • Figure 1: Effective potential $V_\text{eff}(r)$ for charged particles near a SBH: (a) varying $\beta$ with fixed $l$, and (b) varying $l$ with fixed $\beta$. Red points correspond to stable circular orbits, gray points to unstable orbits.
  • Figure 2: Specific energy $\mathcal{E}_c$ versus angular momentum $l_c$ for circular orbits. Solid lines indicate stable orbits, dashed lines unstable orbits. Red points mark the ISCO (see also Table \ref{['Table1']}).
  • Figure 3: Dependence of ISCO parameters on $\beta$: (a) radius $r_\text{ISCO}$, (b) angular momentum $l_\text{ISCO}$, and (c) energy $\mathcal{E}_\text{ISCO}$.
  • Figure 4: Orbital period $T$ versus radius for various magnetic parameters $\beta$.
  • Figure 5: Bound orbits of charged particles for selected $(z,\omega,v)$ and fixed magnetic parameter $\beta$. The black hole is at the origin.