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Extra Dimensions, Nonminimal Couplings, Horizons and Wormholes

Kirill A. Bronnikov
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Abstract

Static, spherically symmetric configurations of gravity with nonminimally coupled scalar fields are considered in D-dimensional space-times in the framework of generalized scalar-tensor theories. We seek special cases when the system has no naked singularity but instead forms either a black hole, or a wormhole. General conditions when this is possible are formulated. In particlar, some such special cases are indicated for multidimensional Brans-Dicke theory and for linear, massless, nonminimally coupled scalar fields. It is shown that in the Brans-Dicke theory the only black-hole solution corresponds to D=4 and the coupling constant ω< -2, and there is a wormhole solution for ω=0. For linear scalar fields it is shown that the only black-hole solution is the well-known one (D=4, a black hole with scalar charge), while the known 4-dimensional wormhole solution is generalized to systems with conformal coupling in arbitrary dimension.

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Kirill A. Bronnikov. 1997-03-07. Extra Dimensions, Nonminimal Couplings, Horizons and Wormholes. https://arxiv.org/abs/gr-qc/9703020

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