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- W4306704808 abstract "We study the periapsis shift of a quasi-circular orbit in a general static spherically symmetric spacetime. 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 $rho_{c}simeq 2.8times 10^{-15} mbox{g}/mbox{cm}^{3} (m/M_{odot})^{2}(r/mbox{au})^{-4}$, 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." @default.
- W4306704808 created "2022-10-19" @default.
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- W4306704808 date "2022-10-14" @default.
- W4306704808 modified "2023-09-26" @default.
- W4306704808 title "General formulae for the periapsis shift of a quasi-circular orbit in a static spherically symmetric spacetime and the active gravitational mass density" @default.
- W4306704808 doi "https://doi.org/10.48550/arxiv.2210.07516" @default.
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