Massless scalar fields and topological black holes

TL;DR

This paper explores new higher-dimensional solutions in Einstein-Maxwell-Klein-Gordon theory, revealing that non-trivial scalar fields typically lead to naked singularities, and compares these with Brans-Dicke black hole solutions.

Contribution

It introduces novel spherically and hyperbolically symmetric solutions in higher dimensions, extending previous four-dimensional models using effective two-dimensional methods.

Findings

New solutions generalize four-dimensional configurations

Non-trivial scalar fields often produce naked singularities

Comparison with higher-dimensional Brans-Dicke solutions

Abstract

The exact static solutions in the higher dimensional Einstein-Maxwell-Klein- Gordon theory are investigated. With the help of the methods developed for the effective dilaton type gauge gravity models in two dimensions, we find new spherically and hyperbolically symmetric solutions which generalize the four dimensional configurations of Dereli-Eris. We show that, like in four dimensions, the non-trivial scalar field yields, in general, a naked singularity. The new solutions are compared with the higher dimensional Brans-Dicke black hole type solutions.