Study on equations of motion for relativistic compact binaries

相对论性致密双星的高精度运动方程在直接探测中子星星双星等相对论性致密双星的引力波中起着至关重要的作用。在本研究计划中，我们利用后牛顿近似，在爱因斯坦广义相对论的3.5阶精度下，导出了相对论性致密双星的运动方程。这是有史以来用第一原理推导出的最精确的运动方程。我们还导出了点电荷在任意电磁场中的运动方程，它与爱因斯坦方程是一致的，因为时空中没有线奇异性。

Highly accurate equations of motion for relativistic compact binaries play an essential role in direct detection of gravitational waves from relativistic compact binaries such as neutron star binaries. In this research project, using the post-Newtonian approximation, we have derived equations of motion for relativistic compact binaries through the 3.5 order accuracy in the Einstein's general relativity. These are the ones of the most accurate equations of motion ever derived using the first principle. We have also derived equations of motion for a point charge in an arbitrary electromagnetic field that is consistent with the Einstein equations by imposing that there be no line-singularity in the space-time.