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

Abstract 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 ( $$e \approx 0.88$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>e</mml:mi> <mml:mo>≈</mml:mo> <mml:mn>0.88</mml:mn> </mml:mrow> </mml:math> ) provides a unique strong-gravity laboratory, yielding a constraint on the tidal charge parameter of $$Q/M^2 = -\,0.29 \pm 0.56$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>/</mml:mo> <mml:msup> <mml:mi>M</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mo>-</mml:mo> <mml:mspace/> <mml:mn>0.29</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.56</mml:mn> </mml:mrow> </mml:math> .