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Generation of Electro and Magneto Static Solutions of the Scalar-Tensor Theories of Gravity

William Bruckman
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Abstract

The field equations of the scalar-tensor theories of gravitation are presented in different representations, related to each other by conformal transformations of the metric. One of the representations resembles the Jordan-Brans-Dicke theory, and is the starting point for the generation of exact electrostatic and magnetostatic exterior solutions. The corresponding solutions for each specific theory can be obtained by transforming back to the original canonical representation, and the conversions are given for the theories of Jordan-Brans-Dicke, Barker, Schwinger, and conformally invariant coupling. The electrostatic solutions represent the exterior metrics and fields of configurations where the gravitational and electric equipotential surfaces have the same symmetry. A particular family of electrostatic solutions is developed, which includes as special case the spherically symmetric solutions of the scalar-tensor theories. As expected, they reduce to the well-known Reissner-Nordström metric when the scalar field is set equal to a constant. The analysis of the Jordan-Brans-Dicke metric yields an upper bound for the mass-radius ratio of static stars, for a class of interior structures.

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William Bruckman. 1994-07-05. Generation of Electro and Magneto Static Solutions of the Scalar-Tensor Theories of Gravity. https://arxiv.org/abs/gr-qc/9407003

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