Effect of Dark Matter Distribution on Scalaron Gravity near the Galactic Center Black Hole and Its Prospects

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.