Electromagnetic plane-wave perturbations in Kasner cosmologies

Maxwell's equations with no sources are solved for the vector potential of electromagnetic plane waves in a Kasner background spacetime (these fields are generally not null). By a transformation of the time coordinate, the one equation not identically zero is transformed into the Euler--Poisson--Darboux equation. The basic theory for this equation and its plane-wave solutions are presented. The stress--energy tensor due to these waves is computed in the limit as the singularity is approached. For some of the wave modes the stress--energy tensor introduces negligible source terms in the perturbation equations for the gravitational field. However, for other wave modes, the stress--energy terms in Einstein's gravitational field equations grow faster as the singularity is approached than the terms due to the Kasner background spacetime. Hence, these wave modes perturb the Kasner background in an unstabilizing manner