Reconstructing Classical Spacetimes from the S-Matrix in Twistor Space

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.