Schwarzschild metric from Scattering Amplitudes to all orders in $G_N$

Stavros Mougiakakos; Pierre Vanhove

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arXiv · 2405.14421

Schwarzschild metric from Scattering Amplitudes to all orders in $G_N$

Stavros Mougiakakos·Pierre Vanhove

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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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Stavros Mougiakakos, Pierre Vanhove. 2024-05-23. Schwarzschild metric from Scattering Amplitudes to all orders in $G_N$. https://arxiv.org/abs/2405.14421

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