Abstract
The Galactic Center star cluster, known as S-stars, is a perfect source of relativistic phenomena observations. The stars are located in the strong field of relativistic compact object Sgr A* and are moving with very high velocities at pericenters of their orbits. In this work we consider motion of several S-stars by using the Parameterized Post-Newtonian (PPN) formalism of General Relativity (GR) and Post-Newtonian (PN) equations of motion of the Feynman’s quantum-field gravity theory, where the positive energy density of the gravity field can be measured via the relativistic pericenter shift. The PPN parameters β and γ are constrained using the S-stars data. The positive value of the Tg00 component of the gravity energy–momentum tensor is confirmed for condition of S-stars motion.
Highlights
The S-stars cluster in the Galactic Center [1,2,3,4] is a unique observable object to investigate
The Post-Newtonian formalism is a tool which provides an opportunity to express the relativistic equations of gravity as the small-order deviations from the Newtonian theory
Our aim was to build a model of the S-stars observations which depends on Parameterized Post-Newtonian (PPN) parameters β and γ
Summary
The S-stars cluster in the Galactic Center [1,2,3,4] is a unique observable object to investigate. Once for the orbital period, the stars pass their pericenters, where they reach high velocities (∼0.01 or even ∼0.1 of the speed of light for the most recent discovered stars [5]) and get close to the relativistic compact object Sgr A*. The purpose of this work is to consider the relativistic Post-Newtonian motion of several S-stars, using the data from the work [25], and to attract attention to the theoretical uncertainty in analysis of PN motion of S-stars due to coordinate dependence of the orbital shapes of the PN test body motion in GR. The effects related to spin of the central massive object, such as Lense–Thirring precession, are detectable via observations of the most recently discovered S-stars [5,26,27]. It is important that we consider only the Schwarzschild problem and do not take the spin-related effects into consideration, which we shall study in separate paper
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