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 (LMS) and High Mass Stars (HMS) . 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 (ELTs). Challenges and prospects associated with the estimations are highlighted.

In this paper, we report the effect of exponential and power-law dark matter density profiles near the Galactic Center black hole on the relative scalaron field amplitude , ψ 0/ϕ (ϕ being Newtonian potential and ψ 0 being the scalaron field amplitude), of f(R) gravity theory. Constraints on the density profiles derived earlier on the basis of orbital motion of the S-2 star are used in conjunction with scalarons having a mass range 10−22–10−16 eV to investigate the dependency of screening or unscreening of modified gravity on the dark matter density through the condition that the rate of pericenter shift due to dark matter is equal to that due to scalaron gravity + general relativistic effects. The semimajor axes are chosen as a = 45 au, 100 au, and 1000 au. It is found that scalarons get screened for extremely low and extremely high mass. This is found to be independent of the black hole spin in the range (χ = 0.1–0.9). For wider orbits scalarons of almost all the masses tend to remain unscreened for the dark matter profiles. It has been found that low dark matter density has a natural tendency to unscreen the scalaron gravity with extremely small coupling strength. We remap screened gravity in the available observational constraints on the scale of modified gravity near the black hole. Astrophysical prospects are presented.

The Galactic center black hole is a putative laboratory to test general relativity (GR) and constrain its alternatives. f(R) scalaron gravity is an interesting alternative to GR and has tremendous prospects for astrophysics and fundamental physics near the black hole. In this work, we search for breaking points of GR through estimation of pericenter shift of stellar orbits with semimajor axis a = (45–1000) au. The black hole spin is taken as the maximum χ = 0.99, and orbital eccentricity is taken as e = 0.9. We work with theoretical scalaron field amplitude and coupling, predicted by Kalita, and also consider the constraints reported by Hees et al. The scalaron mass is taken in the range (10−22–10−17) eV. It is found that GR suppresses scalaron gravity at all orbital radii for the theoretical values of scalaron field coupling predicted by Kalita. Breaking point arises only for higher scalaron coupling resulting from the Hees et al. observations within a few tens of au to a = 1000 au. We also estimate the pericenter shift with a power-law potential V(r) ∼ 1/r 2 arising in five-dimensional gravity and obtain allowed ranges of the five-dimensional Planck mass through existing bounds on the parameterized post-Newtonian parameters coming from the orbits of S-2, S-38, and S-55. The breaking point for GR arises for a five-dimensional Planck mass of about 104 GeV. Constraint on this parameter, expected from the astrometric capabilities of existing and upcoming large telescopes, is also presented.