Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star

TL;DR

This paper uses the observed Schwarzschild precession of the S2 star to constrain parameters of various extended gravity theories, comparing predictions with General Relativity to identify viable models.

Contribution

It introduces a method to estimate parameters of extended gravity theories based on the S2 star's orbital precession, aligning these with GR predictions.

Findings

Power-law f(R) models produce prograde precession similar to GR.

Yukawa-like corrections can mimic GR precession within certain parameter ranges.

Scalar-tensor and non-local gravity theories can also match GR precession under specific conditions.

Abstract

After giving a short overview of previous results on constraining of Extended Gravity (EG) by stellar orbits, we discuss the Schwarzschild orbital precession of S2 star assuming the congruence with predictions of General Relativity (GR). At the moment, the S2 star trajectory is remarkably fitted with the first post-Newtonian (pN) approximation of GR. In particular, both Keck and VLT (GRAVITY) teams declared that the gravitational redshift near its pericenter passage for the S2 star orbit corresponds to theoretical estimates found with the first pN approximation. In 2020, the GRAVITY Collaboration detected the orbital precession of the S2 star around the supermassive black hole (SMBH) at the Galactic Center (GC) and showed that it is close to the GR prediction. Based on this observational fact, we evaluated parameters of the EG theories with the Schwarzschild precession of the S2 star. Using the mentioned method, we estimate the orbital precession angles for some EG models including power-law f(R), general Yukawa-like corrections, scalar-tensor gravity (STG), and non-local gravity (NLG) theories formulated in both metric and Palatini formalism. In this consideration we assume that a gravitational field is spherically symmetric, therefore, alternative theories of gravity could be described only with a few parameters. Specifically, considering the orbital precession, we estimate the range of parameters of these EG models for which the orbital precession is like in GR. We then compare these results with our previous results, which were obtained by fitting the simulated orbits of S2 star to its observed astrometric positions. In case of power-law f(R), generic Yukawa-like correction, STG and NLG theories, we were able to obtain a prograde orbital precession, like in GR. According to these results, the method is a useful tool to evaluate parameters of the gravitational potential at the GC.