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By examining the rate of growth of an invariant volume $\mathcal V$ of some spacetime region along a divergence-free vector field $v^\alpha$, we introduce the concept of a "vector volume" $\mathcal{V}_v$.
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Throughout this paper we use Greek indices to go from 0 to D − 1 D-1 , where D D is the dimensionality of the spacetime; Roman indices usually go from 1 1 to D − 1 D-1 but should be clear in context
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