Establish compatibility of positive- and negative-spin systems with one physical perturbation

Establish whether the separated radiative systems for positive and negative spin weights are compatible representations of a single physical linearized Einstein–Maxwell perturbation, and determine the conditions required for their compatibility.

Background

The paper separately constructs and separates radiative subsystems for positive and negative spin weights. It proves equivalence between each radiative subsystem and its transformed system, but explicitly does not establish that independently selected solutions of the two systems correspond to the same physical perturbation.

Resolving this issue requires identifying the constraints linking the two spin-weight sectors within the full linearized Einstein–Maxwell equations.