论文标题
Bianchi型宇宙引力波中的大地测量和粒子轨迹的偏差
Deviation of geodesics and particle trajectories in a gravitational wave of the Bianchi type VI universe
论文作者
论文摘要
对于Bianchi型VI宇宙，获得了特权坐标系中强原始引力波中测量偏差方程的精确解。该解决方案是指时空的Shapovalov重力波模型，并允许存在用于测试颗粒的汉密尔顿 - 雅各比方程的完整积分。对于获得的所有溶液，获得了强原始引力波中潮汐加速度载体的分析形式。获得了坐标转换的明确形式，即Bianchi型VI宇宙的原始引力波的明确形式，以及实验室同步坐标系中潮汐加速度向量的形式。同步坐标系与自由下落的观察者相关联，使观察者可以分离时间和空间坐标，并可以在空间不同点上同步时间。所提出的数学方法既可以在相对论的一般理论和修改的重力理论中应用。
For the Bianchi type VI universe, exact solutions of the equation of geodesic deviation in a strong primordial gravitational wave in a privileged coordinate system are obtained. The solutions refer to Shapovalov's gravitational-wave models of spacetime and allow the existence of complete integrals of the Hamilton-Jacobi equation for test particles. For all the solutions obtained, the analytical form of the tidal acceleration vector in a strong primordial gravitational wave is obtained. An explicit form of the coordinate transformation, an explicit form of the metric of the primordial gravitational wave of the Bianchi type VI universe, and the form of the tidal acceleration vector in the laboratory synchronous coordinate system are obtained. The synchronous coordinate system is associated with a freely falling observer and allows the observer to separate time and spatial coordinates, as well as to synchronize time at different points in space. The presented mathematical approach can be applied both in the general theory of relativity and in modified theories of gravity.
