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

• Main Authors: de Martino, Ivan, della Monica, Riccardo, de Laurentis, Mariafelicia
• Format: Journal Article
• Language: English
• Published: 12-06-2021
• Subjects: Physics - General Relativity and Quantum Cosmology
• DOI: 10.48550/arxiv.2106.06821

Physical Review D, 104, L101502 (2021) The GRAVITY Collaboration achieved the remarkable detection of the orbital
precession of the S2 star around the Galactic centre supermassive black hole,
providing yet another proof of the validity of the General Relativity. The
departure from the Schwarzschild precession is encoded in the parameter $f_{\rm
SP}$ which multiplies the predicted general relativistic precession. Such a
parameter results to be $f_{\rm SP}=1.10\pm0.19$, which is consistent with
General Relativity ($f_{\rm SP}=1$) at 1$\sigma$ level. Nevertheless, this
parameter may also hide an effect of 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 $f_{\rm SP}$ to constrain the strength and the scale length of the
Yukawa-like potential. No deviation from GR are revealed at scale of
$\lambda<6300$ AU with the strength of the Yukawa potential restricted to
$\delta = -0.01_{-0.14}^{+0.61}$.