Electromagnetic wave propagation in general Kasner-like metrics
  The curved spacetime Maxwell equations are applied to the anisotropically
expanding Kasner metrics. Using the application of vector identities we derive
2$^\textrm{nd}$-order differential wave equations for the electromagnetic field
components; through this explicit derivation, we find that the
2$^\textrm{nd}$-order wave equations are not uncoupled for the various
components (as previously assumed), but that gravitationally-induced coupling
between the electric and magnetic field components is generated directly by the
anisotropy of the expansion. The lack of such coupling terms in the wave
equations from several prior studies may indicate a generally incomplete
understanding of the evolution of electromagnetic energy in anisotropic
cosmologies. Uncoupling the field components requires the derivation of a
4$^\textrm{th}$-order wave equation, which we obtain for Kasner-like metrics
with generalized expansion/contraction rate indices. For the axisymmetric
Kasner case, $(p_{1}, p_{2}, p_{3}) = (1,0,0)$, we obtain exact field solutions
(for general propagation wavevectors), half of which appear not to have been
found before in previous studies. For the other axisymmetric Kasner case,
$\{p_{1}, p_{2}, p_{3}\} = \{(-1/3),(2/3),(2/3)\}$, we use numerical methods to
demonstrate the explicit violation of the geometric optics approximation at
early times, showing the physical phase velocity of the wave to be inhibited
towards the initial singularity, with $v \rightarrow 0$ as $t \rightarrow 0$.
