Classical Solutions and their Double Copy in Split Signature

TL;DR

This paper links three-point scattering amplitudes in split signature spacetime to classical Newman-Penrose scalars, demonstrating a double copy relation that connects gauge theory and gravity solutions, and explores implications for Lorentzian signature.

Contribution

It establishes a novel connection between classical solutions and three-point amplitudes in split signature, and extends the double copy framework to Newman-Penrose scalars and exact metrics.

Findings

Classical objects are Newman-Penrose scalars in split signature.

Double copy of Newman-Penrose scalars matches Weyl double copy.

Exact gravitational metrics derived via Kerr-Schild double copy.

Abstract

The three-point amplitude is the key building block in the on-shell approach to scattering amplitudes. We show that the classical objects computed by massive three-point amplitudes in gauge theory and gravity are Newman-Penrose scalars in a split-signature spacetime, where three-point amplitudes can be defined for real kinematics. In fact, the quantum state set up by the particle is a coherent state fully determined by the three-point amplitude due to an eikonal-type exponentiation. Having identified this simplest classical solution from the perspective of scattering amplitudes, we explore the double copy of the Newman-Penrose scalars induced by the traditional double copy of amplitudes, and find that it coincides with the Weyl version of the classical double copy. We also exploit the Kerr-Schild version of the classical double copy to determine the exact spacetime metric in the gravitational case. Finally, we discuss the direct implication of these results for Lorentzian signature via analytic continuation.