论文标题
将长臂猿抛光方法扩展到绑定的巨大颗粒的轨道
Extending Gibbons-Werner method to bound orbits of massive particles
论文作者
论文摘要
静态球形对称空间中未结合颗粒的重力挠度角的长臂猿 - 妻子方法基于雅各比公制和高斯 - 骨网定理。当将其扩展到结合的巨型颗粒时，存在两个困难：（a）绑定的轨道可能会对自己重叠。为了扩展未结合轨道的挠度角度的定义到绑定的轨道，我们将界限分为多个段，以使每个段不会与自身之间的方位角重叠，并且可以被视为一个未结合的轨道。 （b）在吉本恩斯 - 妻子法中为未结合轨道构建的无限区域对于结合轨道是无效的，因为在遥远的区域，绑定的巨大颗粒的雅各比度量是奇异的。为了构建适合约束轨道的合适区域，我们采用了最后一部作品中提出的广泛的Gibbons-Werner方法[Huang and Cao，https://journals.org.org/prd/prd/prd/prd/prd/prd/prd/physrev.106.106.106.104043]更重要的是，以Schwarzschild时空为例，我们显示了计算的详细信息，并获得了轨道上两个任意点之间偏转角的分析表达。
The Gibbons-Werner method for the gravitational deflection angle of unbound particles in static spherically symmetric spacetimes is based on Jacobi metric and Gauss-Bonnet theorem. When it is extended to bound massive particles, there exists two difficulties: (a) Bound orbits may overlap with themselves azimuthally. To extend the definition of deflection angle for unbound orbits to bound orbits, we divide the bound orbit into multiple segments such that each segment does not overlap with itself azimuthally and can be regarded as an unbound orbit. (b) The infinite region constructed for unbound orbits in Gibbons-Werner method is invalid for bound orbits, since the Jacobi metric of bound massive particles is singular at far region. To construct a suitable region for bound orbits, we adopt the generalized Gibbons-Werner method proposed in our last work [Huang and Cao, https://journals.aps.org/prd/abstract/10.1103/PhysRevD.106.104043], so that the unphysical region in Jacobi space is avoided. What's more, taking the Schwarzschild spacetime as an example, we show the details of the calculation and obtain an analytical expression of the deflection angle between two arbitrary points on the orbit.
