Obtaining the Radiated Gravitational Wave Energy via Relativistic Kinetic Theory: A Kinetic Gas Model of an Idealized Coalescing Binary

Abstract

The final pulse of gravitational wave emission is released in the chirp phase of binary coalescence. This proposes that the radiated energy of the GW is proportional to the chirp mass \(\mathcal{M}\), with detection reports revealing the approximate scaling of \(E_{\mathrm{GW}}\approx\mathcal{M}/10\). While this scaling is evident in numerical relativity, there lacks an analytical expression supporting the relation. This study utilizes a heuristic application of relativistic kinetic theory and massless Bose-Einstein statistics of an entropic graviton gas to GW formation throughout binary coalescence. This approach to GW formation obtains an expression of an effective thermal energy as the radiated GW energy, which extracts the nearly one-tenth scaling of the chirp mass, namely at the chirp phase. Furthermore, it agrees well with the detected energies with 1:1 ratio values ranging from 0.932 for GW150914 to 0.998 for one of three waveform models of GW190521, with 0.851 as an outlier for GW170104. Utilization of a quantum-classical correspondence enabled discussions regarding the usage of equilibrium noise analysis on the graviton gas and kinetic characteristics of the graviton gas during and after coalescence. The latter topic includes, but is not limited to, GW/graviton wave-particle duality, a calculation of the high-energy graviton-graviton total cross section as 1.16% of the chirp mass surface area \(A=16\pi G^2\mathcal{M}^2\), and humoring the thought experiment of black hole gravitons.