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

TL;DR

This paper derives the Schwarzschild black hole metric to all orders in perturbation theory using a novel amplitude-based approach with cubic interactions in general relativity.

Contribution

It introduces a recursion relation for graviton emission form factors, enabling a derivation of the Schwarzschild metric from scattering amplitudes to all orders.

Findings

First derivation of Schwarzschild metric from matter source via amplitudes

Recursion relation for graviton emission form factors

All-order perturbative solution in four dimensions

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.