# Coalescence Time of Compact Binary Systems

## TL;DR

This paper presents an improved analytical formula for estimating the coalescence time of circular compact binary systems, incorporating first post-Newtonian corrections, enhancing accuracy over previous models.

## Contribution

The authors develop a novel analytical solution for coalescence time at 1PN accuracy for circular binaries, improving upon existing approximations.

## Key findings

- The 1PN correction significantly refines coalescence time estimates.
- Comparison shows the improved solution aligns better with numerical results.
- The method extends to arbitrary semi-major axes for circular orbits.

## Abstract

Compact binary systems coalesce over time due to the radiation of gravitational waves, following the field equations of general relativity. Conservation of energy and angular momentum gives a mathematical description for the evolution of separation between the orbiting objects and eccentricity ($e$) of the orbit. We develop an improved analytical solution to the coalescence time for a circular binary system with an arbitrary semi-major axis, to the first post-Newtonian (1PN) accuracy. The results from the quadruple approximation and 1PN approximation are compared for a circular orbit ($e=0$).