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 Center (GC) black hole where the dimensionless gravitational potential ([Formula: see text]) is 100 times stronger than the one encountered in solar system. Therefore, the neighborhood of the GC black hole is a naive opportunity to test modified theories of gravity. In this work, effect of [Formula: see text] gravity near the black hole is studied. The difference of pericenter shift between GR and [Formula: see text] gravity is studied for compact orbits having semi-major axis equal to and below [Formula: see text] au (S0-2 like orbits). In a model-dependent approach, we choose [Formula: see text] (power law gravity) model which is cosmologically motivated and study the deviation in orbital pericenter shift for both zero spin and non-zero spin of the black hole. It is found that effect of [Formula: see text] gravity becomes prominent for compact orbits. In model-independent approach to [Formula: see text] gravity with the generic scalaron fields ([Formula: see text]), we extract the parameters of [Formula: see text] gravity from the current bounds on Parametrized Post-Newtonian (PPN) parameters ([Formula: see text]) near the GC black hole. The screening of [Formula: see text] gravity is also investigated for these bounds on PPN parameters. It has been found that sufficiently massive scalarons ([Formula: see text][Formula: see text]eV) are completely screened but light and intermediate mass scalarons ([Formula: see text][Formula: see text]eV and [Formula: see text][Formula: see text]eV) are unscreened towards S0-2 like orbits as well as in the orbit of the newly discovered short period star S4716 ([Formula: see text][Formula: see text]au). The possibility of detection of the [Formula: see text] gravity effects due to these unscreened scalarons is forecasted with existing and upcoming astrometric capabilities of Extremely Large Telescopes (ELTs).