Effective determinism in a classical field theory with spacelike characteristics

Abstract

For certain classical field theories, it appears as if spacelike characteristic hypersurfaces can occur in the solutions. In principle, this means that acausal propagation is allowed, and the Cauchy problem breaks down. To investigate if indeed this happens, a class of Kasner-like solutions of a generalized Einstein–Maxwell theory is examined. It is found that the spacelike characteristics almost never form, and when they do, they cause no trouble.