Simulation of orbits around the galactic centre black hole with a relativistic Newtonian analogous potential

Abstract

We study the dynamics of a test particle around a central mass taking into account general relativistic effects within the formalism of Lagrangian mechanics, and investigate a real astrophysical object to probe the model. We consider a generalized potential for the Lagrangian of the particle, compute the corresponding equations of motion, and present a numerical scheme to integrate them. Within this approach, we run simulations to fit the orbital parameters of the star S2 around the SMBH Sgr A$^*$, using a Markov Chain Monte Carlo method. We estimate the radius and speed of the star at periapsis, its apsidal precession and the black hole mass. Our results are consistent with results available in previous literature.