论文标题
III型Shapovalov型引力波：粒子轨迹，地球偏差和潮汐加速度
Gravitational Waves of Type III Shapovalov Spacetimes: Particle Trajectories, Geodesic Deviation and Tidal Accelerations
论文作者
论文摘要
对于Shapovalov III型的重力波空间，获得了测量偏差方程和测试颗粒运动方程的确切通用解。解决方案是在特权坐标系中找到的，其中考虑的时空模型的度量取决于波变量。获得了重力波的潮汐加速度的确切形式。在所考虑的时空模型中，可以构建汉密尔顿 - 雅各比方程的完整组成部分。找到了向同步坐标系的过渡的方程式的明确形式，其中选择基础测量粒子上的测试粒子的适当时间作为时间变量，并且时间和空间变量分开。在同步坐标系中，提出了所考虑的波段时期的度量标准形式，获得了测量偏差矢量的形式和潮汐加速度载体。本文中使用的方法和所获得的结果适用于相对论的一般理论和修改的重力理论。提出的方法应用于爱因斯坦的真空方程式。
For gravitational-wave spacetimes of Shapovalov type III, exact general solutions of geodesic deviation equations and equations of motion of test particles are obtained. Solutions are found in a privileged coordinate system, where the metric of the considered spacetime models depends on the wave variable. The exact form of tidal accelerations of the gravitational wave is obtained. In the considered wave models of spacetime, the complete integral of the Hamilton-Jacobi equations of test particles can be constructed. An explicit form of the equations for the transition to a synchronous coordinate system is found, where the proper time of a test particle on the base geodesic is chosen as the time variable, and the time and space variables are separated. In the synchronous coordinate system, the form of the metric of the considered wave spacetime is presented, the form of the geodesic deviation vector and the tidal acceleration vector are obtained. The methods used in the paper and the results obtained are applicable to gravitational waves both in the general theory of relativity and in modified theories of gravity. The proposed approaches are applied to the case of Einstein's vacuum equations.
