On a possible new type of a T odd skewon field linked to   electromagnetism
  In the framework of generally covariant (pre-metric) electrodynamics (``charge & flux electrodynamics''), the Maxwell equations can be formulated in terms of the electromagnetic excitation $H=({\cal D}, {\cal H})$ and the field strength $F=(E,B)$. If the spacetime relation linking $H$ and $F$ is assumed to be {\em linear}, the electromagnetic properties of (vacuum) spacetime are encoded into 36 components of the vacuum constitutive tensor density $\chi$. We study the propagation of electromagnetic waves and find that the metric of spacetime emerges eventually from the principal part $^{(1)}\chi$ of $\chi$ (20 independent components). In this article, we concentrate on the remaining skewon part $^{(2)}\chi$ (15 components) and the axion part $^{(3)}\chi$ (1 component). The skewon part, as we'll show for the first time, can be represented by a 2nd rank traceless tensor $\not S_i{}^j$. By means of the Fresnel equation, we discuss how this tensor disturbs the light cones. Accordingly, this is a mechanism for violating Lorentz invariance and time symmetry. In contrast, the (abelian) axion part $^{(3)}\chi$ does {\em not} interfere with the light cones. 
Friedrich W. Hehl (Cologne), Yuri N. Obukhov (Cologne/Moscow),   Guillermo F. Rubilar (Cologne)