Schwarzschild metric from Scattering Amplitudes to all orders in G_N

2024/05/23 by Stavros Mougiakakos, Pierre Vanhove, Mougiakakos, Stavros +1 · 7 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Pulsars and Gravitational Waves Research

paper · pdf · doi:10.48550/arxiv.2405.14421

openalex publication_date 2024/05/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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