Perturbative spacetimes from Yang-Mills theory

TL;DR

The paper develops a perturbative extension of the BCJ double copy to generate nonlinear gravitational spacetimes from Yang-Mills theory by constructing a fat graviton H_{\mu\nu} and relating it to the conventional skinny fields. It provides explicit first- and second-order perturbative corrections that reproduce JNW-type spacetimes, including Schwarzschild as a Kerr–Schild limit, and introduces a transformation function T^{μν} to connect fat and skinny variables under gauge and field-redefinition freedoms. The method relies on solving YM equations order-by-order, squaring kinematic numerators to obtain fat-graviton data, and then mapping back to h_{μν}, B_{μν}, and φ, with φ tracing the dilaton content. This framework enables a systematic, perturbative bridge from gauge theory to gravity, with potential applications to perturbative black-hole scattering and gravitational radiation, while highlighting the need for an underlying kinematic algebra to streamline higher-order computations.

Abstract

The double copy relates scattering amplitudes in gauge and gravity theories. In this paper, we expand the scope of the double copy to construct spacetime metrics through a systematic perturbative expansion. The perturbative procedure is based on direct calculation in Yang-Mills theory, followed by squaring the numerator of certain perturbative diagrams as specified by the double-copy algorithm. The simplest spherically symmetric, stationary spacetime from the point of view of this procedure is a particular member of the Janis-Newman-Winicour family of naked singularities. Our work paves the way for applications of the double copy to physically interesting problems such as perturbative black-hole scattering.