The Galactic Centre (Sgr A*), hosting a supermassive black hole, carries sufficient potential for testing gravitational theories. Existing astrometric facilities on Very Large Telescope (VLT) and the Keck Telescope have enabled astronomers to study stellar orbits near Sgr A* and perform new astronomical tests of gravitational theories. These observations have provided strong field tests of gravity (ϕ/c2 ∼ 10−3, which is much greater than ϕ/c2 for the Solar system). In this work, we have estimated magnitudes of various contributions to the periastron shift of compact stellar orbits near Sgr A* for pericentre distance in the range rp = (0.3 – 50)au at a fixed orbital inclination, i = 90°. We take the spin of the black hole as χ = 0.1, 0.44, and 0.9 and eccentricities of the orbit as e = 0.9. The relativistic effects including orders beyond 1PN and spin induced effects are incorporated in the contributions. Effect of tidal distortion on periastron shift has also been added into the estimation by considering gravitational Love numbers for polytropic models of the stars. For the tidal effect, we have considered updated mass–radii relations for low-mass stars and high-mass stars. It has been found that the tidal effect on periastron shift arising from stars represented by polytropes of indices n = 1 and n = 3 terminate above rp ∼ 2 au and rp ∼ 1 au, respectively. The periastron shift angle for the stars has been compared with the astrometric capabilities of existing large telescopes and upcoming extremely large telescopes. Challenges and prospects associated with the estimations are highlighted.

中文翻译：

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Sgr A* 附近的广义相对论和潮汐畸变效应导致致密恒星轨道的近天星移动

拥有超大质量黑洞的银河中心 (Sgr A*) 具有足够的潜力来测试引力理论。现有的超大望远镜 (VLT) 和凯克望远镜上的天体测量设备使天文学家能够研究人马座 A* 附近的恒星轨道，并对引力理论进行新的天文测试。这些观测提供了强大的重力场测试（φ/c2 ∼ 10-3，远大于太阳系的 φ/c2）。在这项工作中，我们估计了在固定轨道倾角 i = 90° 范围内 rp = (0.3 – 50)au 范围内的近中心距离对 Sgr A* 附近紧凑恒星轨道的近星移动的各种贡献的大小。我们将黑洞的自旋取为 χ = 0.1、0.44 和 0.9，并将轨道的离心率取为 e = 0.9。相对论效应包括超过 1PN 的阶数和自旋诱导效应被纳入贡献中。通过考虑恒星多变模型的引力 Love 数，潮汐畸变对近星移动的影响也被添加到估计中。对于潮汐效应，我们考虑了低质量恒星和高质量恒星的更新质量-半径关系。已经发现，由指数 n = 1 和 n = 3 的多方体表示的恒星引起的潮汐效应对近星移动的影响分别终止于 rp ∼ 2 au 和 rp ∼ 1 au 之上。恒星的近星移角已与现有大型望远镜和即将推出的超大型望远镜的天体测量能力进行了比较。强调了与估计相关的挑战和前景。