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Main Authors:	Cipriani, Andrea, Di Russo, Giorgio, Fucito, Francesco, Morales, José Francisco, Poghosyan, Hasmik, Poghossian, Rubik
Format:	Preprint
Published:	2025
Subjects:	General Relativity and Quantum Cosmology High Energy Physics - Theory
Online Access:	https://arxiv.org/abs/2501.19257
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author	Cipriani, Andrea Di Russo, Giorgio Fucito, Francesco Morales, José Francisco Poghosyan, Hasmik Poghossian, Rubik
author_facet	Cipriani, Andrea Di Russo, Giorgio Fucito, Francesco Morales, José Francisco Poghosyan, Hasmik Poghossian, Rubik
contents	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.
format	Preprint
id	arxiv_https___arxiv_org_abs_2501_19257
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions Cipriani, Andrea Di Russo, Giorgio Fucito, Francesco Morales, José Francisco Poghosyan, Hasmik Poghossian, Rubik General Relativity and Quantum Cosmology High Energy Physics - Theory 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.
title	Resumming Post-Minkowskian and Post-Newtonian gravitational waveform expansions
topic	General Relativity and Quantum Cosmology High Energy Physics - Theory
url	https://arxiv.org/abs/2501.19257

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