Gravitational bremsstrahlung waveform at the eighth post-Minkowskian order in the extreme-mass-ratio limit

Abstract

The gravitational waveform generated by the scattering of two nonspinning bodies is computed in the frequency domain in the extreme-mass-ratio limit at the eighth post-Minkowskian (PM) order (i.e., $O(G^8)$, or six-loop) and at the fractional sixth post-Newtonian (PN) order. Previous results at $O(G^4)$ are completed here by computing the 5PM radiated angular momentum as well as the 6PM radiation-reacted scattering angle. Up to that order the waveform is expressed in terms of few master integrals, with integrands bilinear in (modified) Bessel functions, leading to iterated Bessel functions which can be in turn expressed in terms of Meijer G functions. Starting from $O(G^5)$ (four-loop) the structure of Fourier integrals becomes quite involved. In fact, there are several new families of master integrals, which can be shown to satisfy inhomogeneous Bessel equations with master integrals of lower order as sources. Although limited to the first order in the mass ratio, the results presented here significantly improve the accuracy of the scattering waveform, currently known at the one-loop level from quantum-amplitude-based computations or at the two-loop level (but with 2PN accuracy only) by using the multipolar-post-Minkowskian formalism.