Deterministic evolution of gauge fields through a singularity

Abstract

The nature of gravitational singularities has been questioned by some recent research, challenging the notion that classical determinism breaks down at these points. By allowing for dynamic changes in the orientation of spatial hypersurfaces, Einstein's equations can be uniquely extended across singularities in certain symmetry-reduced models. A key step in this work was to reformulate the dynamical equations in terms of physical degrees of freedom. The singular behavior, it turns out, is confined to the gauge or unphysical degrees of freedom, and the physical ones evolve smoothly through the singularity. This paper builds on these findings, extending them to a model of gravity coupled with Abelian gauge fields in a homogeneous but anisotropic universe. The study reveals that near the big bang, the dynamics of geometry and gauge fields can be reformulated in a way that preserves determinism, provided there is a change of orientation at the singularity. Intriguingly, the gauge fields are shown to maintain their orientation through the singularity, unlike the spatial hypersurfaces. This suggests that the predicted orientation change of spatial hypersurfaces has physical significance, potentially allowing an observer to determine which side of the big bang they occupy. These results are proved to extend also to non-Abelian gauge fields with only one spatial component.