Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
arXiv:2501.19257 · doi:10.21468/SciPostPhys.19.2.057
Abstract
We derive formulae that resum, at a given order in the soft limit, the infinite series of Post-Minkowskian (small gravitational coupling) or Post-Newtonian (small velocities) corrections to the gravitational waveform produced by particles moving along a general (open or closed) trajectory in the Schwarzschild geometry in the probe limit. Specifying to the case of circular orbits, we compute the waveform and the energy flux to order 30PN, and compare it against the available results in the literature. Our results are based on a novel hypergeometric representation of the solutions of the Heun equation (and its confluence), that leads to a simple mathematical proof of the Heun connection formula.
21 pages + Appendix + References, 2 Figures, 4 Tables; ancillary files are present, containing two Mathematica codes and relative data that are imported within them. Notation has been changed and more references have been added, new version of one ancillary file
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