We study the {\em propagation of electromagnetic waves} in a spacetime devoidof a metric but equipped with a {\em linear} electromagnetic spacetime relation$H\sim\chi\cdot F$. Here $H$ is the electromagnetic excitation $({\cal D},{\calH})$ and $F$ the field strength $(E,B)$, whereas $\chi$ (36 independentcomponents) characterizes the electromagnetic permittivity/permeability ofspacetime. We derive analytically the corresponding Fresnel equation and showthat it is always quartic in the wave covectors. We study the `Fresnel tensordensity' ${\cal G}^{ijkl}$ as (cubic) function of $\chi$ and identify theleading part of $\chi$ (20 components) as indispensable for light propagation.Upon requiring electric/magnetic reciprocity of the spacetime relation, theleading part of $\chi$ induces the {\em light cone} structure of spacetime (9components), i.e., the spacetime metric up to a function. The possibleexistence of an Abelian {\em axion} field (1 component of $\chi$) and/or of a{\em skewon} field (15 components) and their effect on light propagation isdiscussed in some detail. The newly introduced skewon field is expected to beT-odd and related to dissipation.
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机译：我们研究了没有度量标准但配备了{\ em linear}电磁时空关系$ H \ sim \ chi \ cdot F $的时空中的{\ em电磁波传播}。这里$ H $是电磁激励$（{\ cal D}，{\ calH}）$和$ F $的场强$（E，B）$，而$ \ chi $（36个独立分量）则表示电磁电容/时空的渗透性。我们通过解析推导了相应的菲涅耳方程，并证明了它在波矢量中始终是四次的。我们以``\ chi $（立方）函数''形式研究``菲涅耳张力''$ {\ cal G} ^ {ijkl} $，并将$ \ chi $的前导部分（20个分量）确定为光传播必不可少的部分。时空关系的/电磁互易性，$ \ chi $的前导部分引起时空的{\ em light锥}结构（9个分量），即直至一个函数的时空度量。我们详细讨论了一个Abelian {\ em axion}字段（$ \ chi $的1个分量）和/或{\ em skewon}字段（15个分量）的可能存在及其对光传播的影响。新引入的偏斜场有望成为奇数并与耗散有关。
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