Unscreening of f(R) gravity near the galactic center black hole: Testability through pericenter shift below S0-2's orbit

Abstract

General Relativity (GR) has been tested extensively in the solar system and is being tested in the new environment of the Galactic Centre (GC) black hole where the dimensionless gravitational potential ($GM/c^2r$) is 100 times stronger than the one encountered in solar system. Therefore, the neighbourhood of the GC black hole is a naive opportunity to test modified theories of gravity. In this work, effect of $f(R)$ gravity near the black hole is studied. The difference of pericentre shift between GR and $f(R)$ gravity is studied for compact orbits having semi-major axis equal to and below $a=1000$ au (S0-2 like orbits). In a model dependent approach, we choose $f(R) \propto R^2$ (power law gravity) model which is cosmologically motivated and study the deviation in orbital pericentre shift for both zero spin and non-zero spin of the black hole. It is found that effect of $f(R)$ gravity becomes prominent for compact orbits. In model independent approach to $f(R)$ gravity with the generic scalaron fields ($\psi=f'(R)$), we extract the parameters of $f(R)$ gravity from the current bounds on Parametrised Post Newtonian (PPN) parameters ($\gamma , \beta$) near the GC black hole. The screening of $f(R)$ gravity is also investigated for these bounds on PPN parameters. It has been found that sufficiently massive scalarons ($10^{-16}$ eV) are completely screened but light and intermediate mass scalarons ($10^{-22}$ eV and $10^{-19}$ eV) are unscreened towards S0-2 like orbits as well as in the orbit of the newly discovered short period star S4716 ($a=407$ au). The possibility of detection of the $f(R)$ gravity effects due to these unscreened scalarons is forecasted with existing and upcoming astrometric capabilities of Extremely Large Telescopes (ELTs).