Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

TL;DR

This paper develops a holographic method to reconstruct classical gravitational spacetimes from quantum field theory scattering amplitudes using twistor space, connecting quantum amplitudes with classical solutions like black holes.

Contribution

It introduces a new transform from QFT amplitudes to classical spacetimes via twistor space and analytic continuation, linking the double copy in gravity.

Findings

Successfully reconstructs Kerr black hole solutions from amplitudes

Demonstrates the transform for three and four-point amplitudes

Establishes a connection between Kerr-Schild double copy and QFT double copy

Abstract

We present a holographic construction of solutions to the gravitational wave equation starting from QFT scattering amplitudes. The construction amounts to a change of basis from momentum to $(2,2)$ twistor space, together with a recently introduced analytic continuation between $(2,2)$ and $(1,3)$ spacetimes. We test the transform for three and four-point amplitudes in a classical limit, recovering both stationary and dynamical solutions in GR as parametrized by their tower of multipole moments, including the Kerr black hole. As a corollary, this provides a link between the Kerr-Schild classical double copy and the QFT double copy.