Decoupling and integration of general metric-affine EDM PDE systems

Determine whether general decoupling and integration properties can be established for the nonlinear partial differential equation systems describing nonmetric Einstein–Dirac–Maxwell theories formulated on metric-affine manifolds using an arbitrary affine distinguished connection D and Dirac distinguished operator DA (not restricted to canonical nonholonomic variables), in cases where the gamma-matrix decomposition of the metric is not preserved under covariant transports along curves.

Background

In Section 2.3 the paper discusses constructing nonmetric modifications of Einstein–Dirac–Maxwell systems on metric-affine manifolds. When one uses a general affine d-connection D and associated Dirac operator DA (rather than the canonical nonholonomic, metric-compatible choice), the gamma-matrix decomposition is not preserved under covariant transports, which complicates the formulation of consistent spinor dynamics and coupled matter-gravity equations.

The authors note that while their anholonomic frame and connection deformation method (AFCDM) provides decoupling and integration for canonical variables, it is unclear how to achieve such decoupling and integration in full generality for systems built with arbitrary D and DA. This leaves open whether such general systems admit decoupling and integrability properties akin to those obtained in the canonical framework.