摘要
作为两种重要的候选引力理论,广义相对论以及Brans-Dicke引力理论对于理解天体及宇宙的形成与演化具有重要的意义.本文在广义相对论和Brans-Dicke引力理论下,考察恒星附近的行星进动以及星光偏折效应.首先推导出恒星周围的静态球对称背景时空下粒子轨道方程的普适形式;然后分别针对两种引力理论,进一步利用相应的真空场方程的静态球对称精确解推导出描述行星及星光轨道方程,其为非线性的二阶常微分方程;利用微扰法求解轨道方程,得到了含高阶修正的近似解,进而给出了对应的行星进动角和星光偏折角.本文对利用更高精度的实验观测来检验、甄别引力理论具有重要的意义.
As two important alternative theories of gravitation,general relativity and Brans-Dicke's theory,play important roles in our understanding the formation and evolution of celestial bodies and cosmology. In this paper,we study the planet precession and light deflection in general relativity and Brans-Dicke's theory. Firstly,we derive the general orbital equation for a free particle moving in the static,spherically symmetric spacetime by a spherical star. Then,we write down the corresponding equations,which are nonlinear ordinary differential equations of motion for the planet and light ray by using the spherically symmetric solutions to these vacuum field equations in these two theories. Finally,the approximation solutions to the equations of motion can be obtained by the perturbation method,which yield the angles corresponding to the planet precession and light deflection. These results presented in this paper will help us to check and distinguish these two theories of gravity using high-precision experimental observation.
引文
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