Classical solutions and their double copy in split signature

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.

Covariant color-kinematics duality

“…The entirety of our analysis holds at the level of equations of motion. So it is natural to ponder its implications for the classical double copy [33][34][35][36][37][38][39][40][41][42]. Amusingly, covariant colorkinematics duality enforces a trivial version of the classical double copy which applies to any vacuum solution of Einstein's equations and is covertly a restatement of the tetrad formalism.…”

Gauge × gauge = gravity on homogeneous spaces using tensor convolutions

“…Beyond perturbation theory, for particular (e.g. Kerr-Schild) spacetimes there is a non-perturbative classical double-copy of Yang-Mills solutions [52][53][54][55][56], with an elegant variation relating the square of Yang-Mills field strengths to the Weyl tensor [55,[57][58][59][60]. As to applications, there is a vigorous and promising programme to bend amplitudes and the double-copy to the problem of classical black hole scattering in the context of gravity wave astronomy [61][62][63][64][65][66].…”

Note on the asymptotic structure of Kerr-Schild form

“…The complex solutions in the present work are real solutions in the split metric signature (+, +, −, −). The self-dual sector in light-cone coordinates with split signature has very important applications in classical double copy [4,13,31,33]. Other applications of complex solutions can be found, e.g., in [49][50][51].…”