Schwarzschild metric from Scattering Amplitudes to all orders in $G_N$
Abstract
We apply a formulation of Einstein's general relativity with only cubic interactions for deriving the metric of a Schwarzschild black hole to all orders in perturbation theory. This cubic interactions formulation coupled to effective worldline action of a massive point particle allows to derive a recursion relation for the form factors of the off-shell graviton emission current. The unique solution to the recursion relation leads to the Schwarzschild black-hole solution in four dimensions. This provides the first derivation of the black hole metric from a matter source to all orders in perturbation theory from an amplitude approach.
Keywords
Cite
@article{arxiv.2405.14421,
title = {Schwarzschild metric from Scattering Amplitudes to all orders in $G_N$},
author = {Stavros Mougiakakos and Pierre Vanhove},
journal= {arXiv preprint arXiv:2405.14421},
year = {2024}
}
Comments
8 pages. v2: Version to appear in Physical Review letters. Typographically errors corrected. Added an appendix with the explicit form of the recursion relation for the form factors in four dimensions. The general dimensions expressions are on the github repository. Ancillary files available at this repository: https://github.com/pierrevanhove/Metric/tree/main?tab=readme-ov-file#readme