New Approach to Deriving the Schwarzschild Metric Using Scattering Amplitudes

A recent paper titled "Schwarzschild metric from Scattering Amplitudes to all orders in $G_N$" by Stavros Mougiakakos and Pierre Vanhove presents a novel approach to deriving the Schwarzschild black hole metric using a formulation of Einstein's general relativity that incorporates only cubic interactions. This methodology allows for the derivation of the black hole metric to all orders in perturbation theory, which is a significant advancement in theoretical physics.

The authors utilize an effective worldline action of a massive point particle to establish a recursion relation for the form factors of the off-shell graviton emission current. The unique solution to this recursion relation leads to the Schwarzschild black-hole solution in four dimensions. This work marks the first instance of deriving the black hole metric from a matter source using an amplitude approach, which could have implications for understanding black hole physics and gravitational interactions.

The paper, submitted on May 23, 2024, and revised on August 30, 2024, spans eight pages and includes typographical corrections and an appendix detailing the recursion relation for form factors in four dimensions. The findings are set to appear in Physical Review Letters, indicating their relevance and potential impact on the field of high-energy physics and cosmology.

For further details, the paper can be accessed at arXiv:2405.14421.