Complete reconstruction of linearized Einstein–Maxwell perturbations

Construct a full Einstein–Maxwell reconstruction from the separated positive- and negative-spin radiative subsystems, proving that the reconstructed fields satisfy the complete linearized Einstein–Maxwell equations.

Background

The separated equations govern necessary radiative subsystems of the linearized Einstein–Maxwell equations. The paper explicitly notes that the invertible transformations and angular completeness results do not prove that every subsystem solution reconstructs a complete metric and electromagnetic perturbation.

A full reconstruction theorem would establish that the separated radiative data capture the complete physical perturbation system rather than only necessary radiative components.