We compute a revised version of Peters ’ ( 1964 ) time-scale for the gravitational-wave ( GW ) induced decay of two point masses , by taking into account post-Newtonian ( PN ) perturbations of the orbital motion .
At first PN order , the corrected time-scale can be approximated by multiplying Peters ’ estimate by the simple factor Q = 1 + 5 ( r _ { S } / p ) , where p is the periapsis and r _ { S } the Schwarzschild radius of the system .
We apply the revised time-scale to a set of typical LIGO-Virgo and LISA sources at the onset of their GW driven decay .
We argue that our more accurate model for the orbital evolution will affect current event and detection rate estimates for mergers of compact object binaries , with stronger deviations for LISA sources ( EMRIs , IMRIs , and SMBH binaries ) .
We propose the correction factor Q as a simple analytical prescription to quantify decay time-scales more accurately in future population synthesis models .