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

TL;DR

The paper investigates testing f(R) gravity near the Galactic Centre black hole by comparing pericentre shifts of compact stellar orbits to GR predictions. It analyzes a cosmologically motivated f(R) proportional to $R^2$ model and a model-independent scalaron framework, constraining the scalaron amplitude $ψ_0$ via GC PPN bounds on γ and β and identifying screening regimes. The results show that light ($M_ψ = 10^{-22}$ eV) and intermediate ($M_ψ = 10^{-19}$ eV) scalarons can be unscreened for S0-2–like orbits and S4716, producing Yukawa-type deviations that are detectable with current and upcoming astrometric capabilities, while heavy ($M_ψ = 10^{-16}$ eV) scalarons remain screened. These findings provide a pathway to constrain modified gravity in a strong-field regime with ELT-era astrometry, highlighting the role of GC PPN bounds in shaping expected signals.

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 ($ψ=f'(R)$), we extract the parameters of $f(R)$ gravity from the current bounds on Parametrised Post Newtonian (PPN) parameters ($γ, β$) 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).

Figures (6)

• Figure 1: Variation of difference between Schwarzschild and $f(R)$ pericentre shift against semi major axis ($a$) for eccentricity, $e=0.1$ (left figure) and $e=0.9$ (right figure)
• Figure 2: Variation of difference between Kerr and $f(R)$ pericentre shift against semi major axis ($a$) for eccentricity, $e=0.1$ & spin, $\chi=0.1$ (top left figure); $e=0.1$ & $\chi=0.9$ (top right figure); $e=0.9$ & $\chi=0.1$ (bottom left figure) and $e=0.9$ & $\chi=0.9$ (bottom right figure)
• Figure 3: Allowed range of $\psi_0$ for $M_{\psi}=10^{-22}$ eV at $a=45$ au (first and second figures from the left in top row), $a=100$ au (third and fourth figures from the left in top row) and $a=1000$ au (first and second figures from the left in second row); for $M_\psi=10^{-19}$ eV at $a=45$ au (third and fourth figures from the left in second row), $a=100$ au (first and second figures from the left in third row) and $a=1000$ au (third and fourth figures from the left in third row) and for $M_\psi=10^{-16}$ eV at $a=45$ au (first and second figures from the left in bottom row).
• Figure 4: Range of $\psi_0/\phi$ for $M_\psi=10^{-22}$ eV at $a=45$ au (first and second figures from the left in top row), $a=100$ au (third and fourth figures from the left in top row) and $a=1000$ au (first and second figures from the left in second row); for $M_\psi=10^{-19}$ eV at $a=45$ au (third and fourth figures from the left in second row), $a=100$ au (first and second figures from the left in third row) and $a=1000$ au (third and fourth figures from the left in third row) and for $M_\psi=10^{-16}$ eV at $a=45$ au (first and second figures from the left in bottom row).
• Figure 5: Range of $\psi_0/\phi$ in the location of S4716, for $M_\psi=10^{-22}$ eV (first and second figures from the left) and for $M_\psi=10^{-19}$ eV (third and fourth figures from the left).