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Maxwell equations and the optical geometry
1.We adopt the following terminology. An observer is a future-directed, differentiable timelike curve. A reference frame is a congruence of observers, that can also be identified with the field of their four-velocities.
2.We use latin indices , , … from the beginning of the alphabet as abstract indices (see, e.g., Ref. 3), which just indicate the tensorial nature of an object without requiring the specification of a chart. We choose +2 as signature of the metric, for the sign convention of the Levi–Civita tensor and work in units in which .
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13.In spacetimes with a sufficiently high degree of symmetry, this definition turns out to be too weak, and one must supplement it with additional constraints (Ref. 9). However, these considerations do not affect the following discussion, and we shall therefore ignore them.
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