论文标题
静态球形轨道静态轨道偏移的一般公式和静态对称的空间和活性重力质量密度的转移
General formulae for the periapsis shift of a quasi-circular orbit in static spherically symmetric spacetimes and the active gravitational mass density
论文作者
论文摘要
我们研究了一般静态的静态对称空间中的准圆轨道的围绕细胞症。我们相对于重力领域的两个公式，一个公式，一个是在重力质量$ m $和爱因斯坦张量的方面，另一个在轨道角速度和爱因斯坦张量方面。这些公式将众所周知的公式用于Schwarzschild时空的正向转移。在一般情况下，由于爱因斯坦张量的特定组合在轨道的半径$ r $上，因此偏移与真空时空的偏离。由于牛顿重力的扩展质量效应，该公式会向后移动。总体而言，在弱场和弥漫状态中，主动重力质量密度，$ρ_{a} =（ε+p_ {r}+2p_ {t}）/c^{2} $，在$ p_ $，$ p_ {r} $ p_ contrial and contry ne Contriald contry the Contry the Contry the the the Contry the Contrand and the Contry the Contrand and the Contry the Contry the Contry the Contry the Contry the Contry ther物质领域。我们表明，如果$ρ_{a} $超出关键值$ρ_{c} \ simeq 2.8 \ times 10^{ - 15} \ mbox {g}/\ mbox {cm}^{3} {3} （m/m _ {\ odot}）^{2}（r/\ mbox {au}）^{ - 4} $，而向前移动比真空时空中的转移大于$ρ_{a} <0 $，即，即强烈的能量条件，因此提供了强烈的能量，因此可以证明深色能量。我们在太阳系和银河系中心的$ρ_{a} $上获得了新的观测约束。
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, $ρ_{A}=(ε+p_{r}+2p_{t})/c^{2}$, plays an important role, where $ε$, $p_{r}$, 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 $ρ_{A}$ is beyond a critical value $ρ_{c}\simeq 2.8\times 10^{-15} \mbox{g}/\mbox{cm}^{3} (m/M_{\odot})^{2}(r/\mbox{au})^{-4}$, while a forward shift greater than that in the vacuum spacetime instead implies $ρ_{A}<0$, i.e., the violation of the strong energy condition, and thereby provides evidence for dark energy. We obtain new observational constraints on $ρ_{A}$ in the Solar System and the Galactic Centre.
