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

TL;DR

This paper explores how the shape and properties of black hole shadows in $f(R)$ gravity can reveal deviations from General Relativity, using analytical models and observational constraints.

Contribution

It provides an analytical model of Galactic Center black holes in $f(R)$ gravity, linking scalaron mass to observable shadow features and weak field tests.

Findings

Shadow shape is sensitive to scalaron mass even at low spin.

Scalaron mass compatible with Kerr quadrupole moment and solar system constraints.

Scalaron masses consistent with S-star observations and general relativistic limits.

Abstract

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.