Comments on Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to S2 star orbit, arXiv:2406.03371v2

TL;DR

This paper critiques a recent study on particle orbits with magnetic dipole moments near magnetized Schwarzschild black holes, highlighting derivation inconsistencies that affect the equations of motion.

Contribution

It provides a detailed analysis of the Hamilton-Jacobi formulation and identifies errors in the original work's interaction term usage.

Findings

Identified inconsistencies in the original Hamilton-Jacobi derivation.

Showed that the original equations of motion are incorrect due to these inconsistencies.

Clarified the correct formulation for particles with magnetic dipole moments near black holes.

Abstract

We provided comments on the article Orbits of particles with magnetic dipole moment around magnetized Schwarzschild black holes: Applications to S2 star orbit by Uktamjon Uktamov, Mohsen Fathi, Javlon Rayimbaev, and Ahmadjon Abdujabbarov from arXiv:2406.03371v2. We derived the Hamilton-Jacobi equation used in the article from the Lagrangian utilized and found inconsistencies in the use of the interaction term which describes the magnetic dipole moment of the particle. Consequently, this results in incorrect equations of motion for the particle.