Persistence of the contracting Bianchi I attractor with torsion

Determine whether the contracting Bianchi I attractor persists when the Einstein–Dirac dynamical-systems analysis is extended to Einstein–Cartan gravity with torsion.

Background

The paper analyzes self-gravitating Dirac fields in LRS III spacetimes within General Relativity and finds that the cosmological evolution asymptotically approaches a contracting Bianchi I spacetime. The authors identify Riemann–Cartan geometry, particularly Einstein–Cartan gravity, as a natural extension because torsion couples directly to the intrinsic spin of the Dirac field.

The unresolved issue is whether the attractor structure found in the torsion-free Einstein–Dirac system survives after torsion is included. Resolving this would clarify the robustness of the paper’s asymptotic result in a theory more directly incorporating the spin of the Dirac field.