On the 2PN pericentre precession in the general theory of relativity and the recently discovered fast orbiting S-stars in Sgr A${}^{\ast }$

Abstract

Recently, the secular pericentre precession was analytically computed to the second post-Newtonian (2PN) order by the present author with the Gauss equations in terms of the osculating Keplerian orbital elements in order to obtain closer contact with the observations in astronomical and astrophysical scenarios of potential interest. A discrepancy with previous results by other authors was found. Moreover, some of such findings by the same authors were deemed as mutually inconsistent. In this paper, it is demonstrated that, in fact, two calculational errors plagued the most recent calculation by the present author. They are explicitly disclosed and corrected. As a result, all the examined approaches mutually agree yielding the same analytical expression for the total 2PN pericentre precession once the appropriate conversions from the adopted parameterizations are made. It is also shown that, in future, it may become measurable, at least in principle, for some of the recently discovered short-period S-stars in Sgr A${}^{\ast }$ like S62 and S4714.

LaTex2e, 15 pages, 1 table, 1 figure. Typo in Eq.(7) of the previous version, equal to Eq.(53) in Iorio L., 2020, Universe, 6, 53, corrected. Eqs. (25)-(26) correct Eqs. (51)-(52) in Iorio L., 2020a, Universe, 6, 53. Accepted for publication in Universe

References in corpus (9)

• The Confrontation between General Relativity and Experiment
• Detection of the Schwarzschild precession in the orbit of the star S2 near the Galactic centre massive black hole
• S62 and S4711: Indications of a population of faint fast moving stars inside the S2 orbit -- S4711 on a 7.6 year orbit around Sgr~A*
• An upper limit on the spin of SgrA${}^{\ast }$ based on stellar orbits in its vicinity
• Apoastron Shift Constraints on Dark Matter Distribution at the Galactic Center
• The short-period S-stars S4711, S62, S4714 and the Lense-Thirring effect due to the spin of Sgr A${}^{\ast }$
• The Orbital Pericenter Precession in the 2PN Approximation
• Revisiting the 2PN pericentre precession in view of possible future measurements of it
• Post-Newtonian Theory and its Application

Cited by in corpus (5)

• Estimating the Parameters of Extended Gravity Theories with the Schwarzschild Precession of S2 Star
• Estimating the parameters of Hybrid Palatini gravity model with the Schwarzschild precession of S2, S38 and S55 stars: case of bulk mass distribution
• Orbital precession of stars in the Galactic center
• Analysis of the PPN Two-Body Problem Using Non-Osculating Orbital Elements
• On the 2PN periastron precession of the Double Pulsar PSR J0737-3039A/B