Analytical coordinate time at first post-Newtonian order

TL;DR

This paper derives an analytical expression for coordinate time at first post-Newtonian order using the Damour-Deruelle solution, aiding pulsar timing and gravitational-wave research.

Contribution

It provides a new analytical formula relating coordinate time and polar angle at first post-Newtonian order, enhancing theoretical tools in astrophysics.

Findings

Analytical expression for coordinate time derived

Applicable to pulsar timing and gravitational waves

Improves theoretical modeling accuracy

Abstract

In this letter, we exploit the Damour-Deruelle solution to derive the analytical expression of the coordinate time in terms of the polar angle. This formula has advantageous applications in both pulsar timing and gravitational-wave theory.