Weyl double copy in bimetric massive gravity

TL;DR

The paper develops and applies the Weyl double copy (WDC) framework to Hassan–Rosen bigravity, distinguishing Type D (no massive Weyl modes) from Type N (incorporating massive BG modes). By leveraging a Kerr–Schild (KS) ansatz, the authors connect gravity solutions in bigravity to corresponding gauge and scalar theories, obtaining Maxwell and conformally coupled Klein–Gordon dynamics for Type D, and Proca-type plus massive Klein–Gordon dynamics for Type N. They analyze both vacuum and matter-coupled configurations, including dyonic Kerr–Newman–(A)dS and Plebański–Demiański, as well as BG analogs of pp-waves and Siklos waves, highlighting how resonance masses arise from matter content. The results reveal a clean separation of GR-like contributions and BG-induced massive sectors, offering a practical route to study classical double copy in a ghost-free massive gravity context and suggesting further exploration beyond KS spacetimes.

Abstract

The Weyl double copy formalism, which relates the Weyl spinor with the square of the field strength, is studied in the context of Hassan-Rosen bigravity for stationary and time-dependent solutions. We consider the dyonic Kerr-Newman-(A)dS solution and the Plebański-Demiański metric in the context of bigravity. These solutions are studied in the Weyl double copy both with matter independently coupled and show that no massive modes are present in the Weyl spinor. The equations of motion for the gauge and scalar fields are those of Maxwell equations coupled to an external source, and massless Klein-Gordon equations with a conformal curvature term and an external source, all of them consistent with general relativity. For wave solutions, massive modes are manifest in the Weyl spinor and a formulation in bigravity for these massive modes is proposed. The resulting equations of motion are Proca equations with a conformal term and massive Klein-Gordon equations. In the case of the matter contributions for waves, we show how the resonance mass is present in equations of motion of the fields obtained from the Weyl double copy. The solutions studied are written in a Kerr-Schild form, connecting with the Kerr-Schild double copy.