线性预度规电动力学与光锥的推导
Linear pre-metric electrodynamics and deduction of the light cone
摘要：
我们制定了一个通用的框架来描述时空的电磁特性。这些性质被编码在"真空的本构张量"中，这是一个类似于描述物质介质所用的量。我们给出了一个一般的协变推导的菲涅耳方程描述的局部性质的电磁波的传播的情况下，最一般的可能的线性本构张量。我们还研究了光锥结构的诱导和这种结构出现的情况下的特殊情况。特别地，我们将研究在一定条件下由本构张量定义的对偶算子与共形度量的存在性之间的关系。封闭性和对称性的本构张量将被发现的条件，确保存在的共形度量。我们还将看到，如果满足这两个条件，如何从本构张量显式推导出度量分量。最后，我们将用同样的方法来探索放松对称条件的后果，以及这如何影响光锥的出现。
英文摘要：
We formulate a general framework for describing the electromagnetic properties of spacetime. These properties are encoded in the `constitutive tensor of the vacuum', a quantity analogous to that used in the description of material media. We give a generally covariant derivation of the Fresnel equation describing the local properties of the propagation of electromagnetic waves for the case of the most general possible linear constitutive tensor. We also study the particular case in which a light cone structure is induced and the circumstances under which such a structure emerges. In particular, we will study the relationship between the dual operators defined by the constitutive tensor under certain conditions and the existence of a conformal metric. Closure and symmetry of the constitutive tensor will be found as conditions which ensure the existence of a conformal metric. We will also see how the metric components can be explicitly deduced from the constitutive tensor if these two conditions are met. Finally, we will apply the same method to explore the consequences of relaxing the condition of symmetry and how this affects the emergence of the light cone.
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