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Let K be a Killing vector field. Show that an electromagnetic field with potential Aj=Kμ solves Maxwell's equations if the metric is a vacuum solution to Einstein's equations. This is a slight cheat, since you won't be in vacuum if there is a nonzero electromagnetic field strength, but we assume the field strength is small enough not to dramatically affect the geometry. | Numerade
Let K be a Killing vector field. Show that an electromagnetic field with …
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