Volume elements of spacetime and a quartet of scalar fields

Details Volume elements of spacetime and a quartet of scalar fields Volume elements of spacetime and a quartet of scalar fields

1997-12-15

arxiv.org/abs/gr-qc/9712063v1

Phys.Rev. D58 (1998) 084021

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages RevTEX, submitted to Phys. Rev. D

Scientific paper

10.1103/PhysRevD.58.084021

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 \sigma. 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 \sigma as 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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