Geometrization Conditions for Perfect Fluids, Scalar Fields, and Electromagnetic Fields
Abstract
Rainich-type conditions giving a spacetime "geometrization" of matter fields in general relativity are reviewed and extended. Three types of matter are considered: perfect fluids, scalar fields, and electromagnetic fields. Necessary and sufficient conditions on a spacetime metric for it to be part of a perfect fluid solution of the Einstein equations are given. Formulas for constructing the fluid from the metric are obtained. All fluid results hold for any spacetime dimension. Geometric conditions on a metric which are necessary and sufficient for it to define a solution of the Einstein-scalar field equations and formulas for constructing the scalar field from the metric are unified and extended to arbitrary dimensions, to include a cosmological constant, and to include any self-interaction potential. Necessary and sufficient conditions on a four-dimensional spacetime metric for it to be an electrovacuum and formulas for constructing the electromagnetic field from the metric are generalized to include a cosmological constant. Both null and non-null electromagnetic fields are treated. A number of examples and applications of these results are presented.
Keywords
Cite
@article{arxiv.1503.06311,
title = {Geometrization Conditions for Perfect Fluids, Scalar Fields, and Electromagnetic Fields},
author = {D. S. Krongos and C. G. Torre},
journal= {arXiv preprint arXiv:1503.06311},
year = {2015}
}
Comments
28 pages, no figures