Study on equations of motion for relativistic compact binaries

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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.