Gravitational Bremsstrahlung Waveform at the fourth Post-Minkowskian order and the second Post-Newtonian level
| Autor: | Bini, Donato, Damour, Thibault, Geralico, Andrea |
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| Rok vydání: | 2024 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Using the Multipolar Post-Minkowskian formalism, we compute the frequency-domain waveform generated by the gravitational scattering of two nonspinning bodies at the fourth post-Minkowskian order ($O(G^4)$, or two-loop order), and at the fractional second Post-Newtonian accuracy ($O(v^4/c^4)$). The waveform is decomposed in spin-weighted spherical harmonics and the needed radiative multipoles, $U_{\ell m}(\omega), V_{\ell m}(\omega)$, are explicitly expressed in terms of a small number of master integrals. The basis of master integrals contains both (modified) Bessel functions, and solutions of inhomogeneous Bessel equations with Bessel-function sources. We show how to express the latter in terms of Meijer G functions. The low-frequency expansion of our results is checked againg existing classical soft theorems. We also complete our previous results on the $O(G^2)$ bremsstrahlung waveform by computing the $O(G^3)$ spectral densities of radiated energy and momentum, in the rest frame of one body, at the thirtieth order in velocity. Comment: 22 pages, revtex macros used |
| Databáze: | arXiv |
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