Extra Dimensions, Nonminimal Couplings, Horizons and Wormholes

TL;DR

This paper explores conditions under which higher-dimensional gravity theories with nonminimally coupled scalar fields produce black holes or wormholes, identifying specific solutions and their dimensional constraints.

Contribution

It provides a comprehensive analysis of static, spherically symmetric solutions with nonminimal scalar couplings, highlighting conditions for horizon and wormhole formation in multidimensional theories.

Findings

In Brans-Dicke theory, only 4D with mbda< -2 yields black holes.

A wormhole exists for mbda=0 in Brans-Dicke theory.

The 4D wormhole solution is extended to arbitrary dimensions with conformal coupling.

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 \omega< -2, and there is a wormhole solution for \omega=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.