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

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. Finally, we test our model by fitting it to real data from the observed trajectory of the S2 star using a statistical Markov Chain Monte Carlo (MCMC) method. This allows us to find the best estimates for magnetic field and charge of the S2 star.

💡 Research Summary

The paper investigates the motion of charged particles in the spacetime of a Schwarzschild black hole that is immersed in an external, asymptotically uniform magnetic field. Using Wald’s prescription for the electromagnetic four‑potential, the authors construct the Lagrangian for a particle of mass m and charge q, and derive the equations of motion via the Hamilton–Jacobi formalism. By restricting the dynamics to the equatorial plane, they obtain a conserved specific energy E, a specific angular momentum l, and a magnetic parameter β = qB/(2m). The radial motion is governed by an effective potential
(V_{\rm eff}(r)=f(r)\Big