论文标题
在静止时的单极和四极杆场中的2pn近似中的光传播：初始值问题
Light propagation in 2PN approximation in the monopole and quadrupole field of a body at rest: Initial value problem
论文作者
论文摘要
在第二个牛顿后（2pn）近似中确定了一个静止和四极结构的一个身体的重力场中的光轨迹。光线的测量方程中的术语分为与时间无关的紧张系数和四种时间依赖的标量函数。因此，在每种情况下，地球方程的第一和第二集成只能将其减少到四种标量主积分。这些积分可以通过复发关系以封闭形式解决。单极和四极杆的2pn条款贡献了$ 1 $ nano-arcsecond的总光偏转。但是，在单极和四极杆的情况下，在2pn的光偏转中都有增强的术语。这些增强的2PN项是由使用冲击向量引起的，这对于对实际星体测量值进行建模是必不可少的。如果在木星和土星上放牧光线，则由人体四极结构引起的增强的2pn项，分别高达0.95个微弧形和0.29微弧形。因此，2Pn四极术语与在精确度的亚微弧形尺度上的高精度天文统计有关。
The light trajectory in the gravitational field of one body at rest with monopole and quadrupole structure is determined in the second post-Newtonian (2PN) approximation. The terms in the geodesic equation for light rays are separated into time-independent tensorial coefficients and four kind of time-dependent scalar functions. Accordingly, the first and second integration of geodesic equation can be reduced in each case to only four kind of scalar master integrals. These integrals can be solved in closed form by recurrence relations. The 2PN terms of monopole and quadrupole contribute less than $1$ nano-arcsecond to the total light deflection. There are, however, enhanced terms in the 2PN light deflection, both in case of monopole and quadrupole. These enhanced 2PN terms are caused by the use of an impact vector which is indispensable for modeling of real astrometric measurements. In case of grazing light rays at Jupiter and Saturn, the enhanced 2PN terms, caused by the quadrupole structure of the body, amount up to 0.95 micro-arcseconds and 0.29 micro-arcseconds, respectively. Thus, the 2PN quadrupole terms are relevant for high-precision astrometry on the sub-micro-arcsecond scale of accuracy.
