Graviton Number Radiated During Binary Inspiral

Abstract

The total number of gravitons emitted during nonrelativistic inspiral of two black holes or other effectively point masses is calculated approximately and found to be remarkably close to (well within 1% of, perhaps within about 0.2% of) the initial orbital angular momentum divided by the spin angular momentum of each graviton ($2\hslash$), although at unit initial eccentricity, $2\hslash$ times the initial graviton number emission per angular momentum emission is $248/(45\sqrt{3}\pi )\approx 1.012811600479$, almost 1.3% greater than unity.

16 pages, 7 typos corrected and Note Added about results extended by Y.~Chung and H.~S.~Yang, arXiv:2409.14808