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arXiv · gr-qc/9712063

Volume elements of spacetime and a quartet of scalar fields

Frank Gronwald·Uwe Muench·Alfredo Macías·Friedrich W. Hehl
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Abstract

Starting with a `bare' 4-dimensional differential manifold as a model of spacetime, we discuss the options one has for defining a volume element which can be used for physical theories. We show that one has to prescribe a scalar density σ. Whereas conventionally \sqrt{|\det g_{ij}|} is used for that purpose, with g_{ij} as the components of the metric, we point out other possibilities, namely σas a `dilaton' field or as a derived quantity from either a linear connection or a quartet of scalar fields, as suggested by Guendelman and Kaganovich.

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Frank Gronwald, Uwe Muench, Alfredo Macías, Friedrich W. Hehl. 1997-12-15. Volume elements of spacetime and a quartet of scalar fields. https://doi.org/10.1103/physrevd.58.084021

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