special relativity - Covariant Description of Light Scattering at a fastly rotating Cylinder

Let us consider the following Gedankenexperiment:

A cylinder rotates symmetric around the $z$ axis with angular velocity $\Omega$ and a plane wave with $\mathbf{E}\text{, }\mathbf{B} \propto e^{\mathrm{i}\left(kx - \omega t \right)}$ gets scattered by it.

We assume to know the isotropic permittivity $\epsilon(\omega)$ and permeability $\mu(\omega)$ of the cylinder's material at rest. Furthermore, the cylinder is infinitely long in $z$-direction.

The static problem ($\Omega = 0$) can be treated in terms of Mie Theory - here, however, one will need a covariant description of the system for very fast rotations (which are assumed to be possible) causing nontrivial transformations of $\epsilon$ and $\mu$.

Hence my question:

What is the scattering response to a plane wave on a fastly rotating cylinder?

RotatingDisc http://www.personal.uni-jena.de/~p3firo/PhysicsSE/RotatingDisc.png

Thank you in advance