Multiparticle solutions to Einstein's equations

TL;DR

This paper introduces the first multiparticle solutions to Einstein's equations with matter, using a novel perturbiner method to simplify calculations of tree-level amplitudes involving gravitons and matter in any dimension.

Contribution

It presents a new iterative approach to solve Einstein's equations for multiple particles, enabling efficient computation of scattering amplitudes with matter and gravitons.

Findings

First multiparticle solutions to Einstein's equations with matter.

A perturbiner-based method simplifies amplitude calculations.

Applicable to any spacetime dimension and matter content.

Abstract

In this letter we present the first multiparticle solutions to Einstein's field equations in the presence of matter. These solutions are iteratively obtained via the perturbiner method, which can circumvent gravity's infinite number of vertices with the definition of a multiparticle expansion for the inverse spacetime metric as well. Our construction provides a simple layout for the computation of tree level field theory amplitudes in $D$ spacetime dimensions involving any number of gravitons and matter fields, with or without supersymmetry.