تقرير
General formulae for the periapsis shift of a quasi-circular orbit in static spherically symmetric spacetimes and the active gravitational mass density
| العنوان: | General formulae for the periapsis shift of a quasi-circular orbit in static spherically symmetric spacetimes and the active gravitational mass density |
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| المؤلفون: | Harada, Tomohiro, Igata, Takahisa, Saida, Hiromi, Takamori, Yohsuke |
| المصدر: | International Journal of Modern Physics D Vol. 32, No. 15 (2023) 2350098 (20 pages) |
| سنة النشر: | 2022 |
| المجموعة: | Astrophysics General Relativity and Quantum Cosmology High Energy Physics - Theory |
| مصطلحات موضوعية: | General Relativity and Quantum Cosmology, Astrophysics - Astrophysics of Galaxies, Astrophysics - High Energy Astrophysical Phenomena, Astrophysics - Solar and Stellar Astrophysics, High Energy Physics - Theory |
| الوصف: | We study the periapsis shift of a quasi-circular orbit in general static spherically symmetric spacetimes. We derive two formulae in full order with respect to the gravitational field, one in terms of the gravitational mass $m$ and the Einstein tensor and the other in terms of the orbital angular velocity and the Einstein tensor. These formulae reproduce the well-known ones for the forward shift in the Schwarzschild spacetime. In a general case, the shift deviates from that in the vacuum spacetime due to a particular combination of the components of the Einstein tensor at the radius $r$ of the orbit. The formulae give a backward shift due to the extended-mass effect in Newtonian gravity. In general relativity, in the weak-field and diffuse regime, the active gravitational mass density, $\rho_{A}=(\epsilon+p_{r}+2p_{t})/c^{2}$, plays an important role, where $\epsilon$, $p_{r}$, and $p_{t}$ are the energy density, the radial stress, and the tangential stress of the matter field, respectively. We show that the shift is backward if $\rho_{A}$ is beyond a critical value $\rho_{c}\simeq 2.8\times 10^{-15} \mbox{g}/\mbox{cm}^{3} (m/M_{\odot})^{2}(r/\mbox{au})^{-4}$, while a forward shift greater than that in the vacuum spacetime instead implies $\rho_{A}<0$, i.e., the violation of the strong energy condition, and thereby provides evidence for dark energy. We obtain new observational constraints on $\rho_{A}$ in the Solar System and the Galactic Centre. Comment: 25 pages, minor revision, discussion expanded, accepted for publication in the International Journal of Modern Physics D |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1142/S0218271823500980 |
| URL الوصول: | http://arxiv.org/abs/2210.07516 |
| رقم الأكسشن: | edsarx.2210.07516 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1142/S0218271823500980 |
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