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

Duško Borka,Salvatore Capozziello,Predrag Jovanović,Vesna Borka Jovanović,Alexander F Zakharov

doi:10.3390/universe7110407

Abstract

After giving a short overview of previous results on constraining of Extended Gravity 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 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 post-Newtonian (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 and showed that it is close to the GR prediction. Based on this observational fact, we evaluated parameters of the Extended Gravity theories with the Schwarzschild precession of the S2 star. Using the mentioned method, we estimate the orbital precession angles for some Extended Gravity models including power-law f(R), general Yukawa-like corrections, scalar–tensor gravity, and non-local gravity 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 Extended Gravity models for which the orbital precession is like in GR. Then we 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, scalar–tensor gravity and non-local gravity 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 Galactic Center.

Highlights

Several modified gravity theories have been proposed as possible extensions of Einstein’s theory of gravity [1]
We first give a short overview of our previous results regarding the study of the extending theories of gravity by the observed orbit of the S2 star, and we will evaluate parameters of Rn, Yukawa, Sanders, Palatini and non-local gravity theories with the Schwarzschild precession of the S2 star, i.e., by assuming that the orbital precession of the S2 star is equal to the corresponding theoretical quantity calculated in General Relativity (GR)
In order to calculate the precession of the S2 star in modified gravity, we assume that the weak field potential does not differ significantly from the Newtonian potential

Summary

Introduction

Several modified gravity theories have been proposed as possible extensions of Einstein’s theory of gravity [1] Among their main motivations, there is the possibility to explain cosmological and astrophysical data at different scales without introducing dark energy and dark matter, but just taking into account further degrees of freedom of the gravitational field emerging from geometric corrections [2]. Different alternative approaches for the weak field limit starting from fourth-order theories of gravity, like f (R), have been proposed and discussed [17,18,19,20,21,22,23,24,25,26]. Some experimental limits related to Extended Theories of Gravity are reported in the literature [28,29,30,31]

Objectives

Results

Conclusion