High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries

Understand

The post-Newtonian approximation is still the most widely used approach to obtaining explicit solutions in general relativity, especially for the relativistic two-body problem with arbitrary mass ratio.

• Within many of its applications, it is often required to use a regularization procedure.
• Though frequently misunderstood, the regularization is essential for waveform generation without reference to the internal structure of orbiting bodies.
• In recent years, direct comparison with the self-force approach, constructed specifically for highly relativistic particles in the extreme mass ratio limit, has enabled preliminary confirmation of the foundations of both computational methods, including their very independent regularization procedures, with high numerical precision.