Effects of tidal charge on orbital motion in DMPR brane-world black holes

In this work, the orbital energy and angular momentum are calculated based on the DMPR brane-world black holes, followed by the derivation of the solution for the motion of a test particle to the second post-Newtonian order. The charge parameter Q is found to influence both the periastron advance and orbital period. In particular, its effect on perihelion precession is observed at both the first and second post-Newtonian orders, while the impact on the orbital period occurs only at the second post-Newtonian order. Furthermore, the validity of our model is confirmed by analyzing the pericenter precession of the star S2 orbiting the Galactic Center supermassive black hole Sgr A*. This nearby high-eccentricity orbit ( e ≈ 0.88 e ≈ 0.88 ) provides a unique strong-gravity laboratory, yielding a constraint on the tidal charge parameter of Q/M² = -\,0.29 ± 0.56 Q / M 2 = - 0.29 ± 0.56 .