Black hole based general relativistic limit of f(R) theory of gravity

The Galactic Center black hole environment gives us new opportunity to test deviation from General Relativity and black hole physics. In this work we analytically generate the shape of the Galactic Center black hole by using a recently developed exact stationary, axisymmetric and vacuum solution of $f(R)$ gravity theory. By using scalaron mass as a free parameter we find that the shadow shape along with displacement and asymmetry is sensitive to the scalaron mass, even after keeping the black hole spin low. We recognize scalaron mass which is compatible with Kerr like quadrupole moment and hence black hole “no-hair” theorem. The same mass scale is found to reproduce the PPN parameter ($\gamma$) constrained in the weak field limit of the solar system. Gravitational identifiers, the Kretschmann scalar ($\kappa$) and gravitational potential ($\phi$) have been used to infer scalaron masses in the regime of S-stars which are found to be consistent with the limits obtained using shadow scales. We ensure that $f(R)$ gravity scalaron has an appropriate general relativistic limit in the horizon scale of the black hole. We also identify the possibility of scale invariance of the general relativistic limit.