$f(R)$ gravity after the detection of the orbital precession of the S2 star around the Galactic Center massive black hole

The GRAVITY Collaboration achieved a remarkable detection of the orbital precession of the S2 star around the Galactic Center supermassive black hole, providing yet another proof of the validity of general relativity. The departure from the Schwarzschild precession is encoded in the parameter $f_{\mathrm{SP}}$, which multiplies the predicted general relativistic precession. This parameter results in $f_{\mathrm{SP}}=1.10\pm 0.19$, which is consistent with general relativity ($f_{\mathrm{SP}}=1$) at $1\sigma$ level. Nevertheless, this parameter may also hide an effect of the modified theories of gravity. Thus, we consider the orbital precession due to the Yukawa-like gravitational potential arising in the weak field limit of $f(R)$-gravity, and we use the current bound on the $f_{\mathrm{SP}}$ to constrain the strength and the scale length of the Yukawa-like potential. No deviations from general relativity are revealed at the scale of $\lambda <6300\mathrm{AU}$ with the strength of the Yukawa potential restricted to $\delta =-{0.01}_{-0.14}^{+0.61}$.

Figure 1

68%, 95%, and 99% confidence levels of the posterior probability density distributions for the two $f(R)$-gravity parameters $\{\delta ,\lambda \}$. Top: posterior distributions are based only on data from [49]. Bottom: data include also the measurement of the precession provided by GRAVITY Collaboration [34]. This is an inset of the whole corner plot presented in Fig. 5 in the SM.