Brans-Dicke-Maxwell Solutions for Higher Dimensional Static Cylindrical Symmetric Spacetime

TL;DR

This paper derives exact Brans-Dicke-Maxwell solutions for higher-dimensional static cylindrical spacetimes with magnetic fields, exploring their relation to Einstein frame solutions and general relativity limits.

Contribution

It provides new exact solutions for higher-dimensional Brans-Dicke-Maxwell spacetimes with cylindrical symmetry, including their relation to dilaton and Einstein frame solutions.

Findings

Solutions reduce to Dilaton-Melvin spacetime in a special case

General relativity limit differs from four-dimensional case

Solutions include azimuthal magnetic field configurations

Abstract

In this paper, Brans-Dicke-Maxwell type vacuum solutions are considered for a static cylindrically symmetric spacetime in arbitrary dimensions. Exact solutions are obtained by directly solving the field equations for the case where an azimuthal magnetic field is present. Other configurations such as axial magnetic field case can be obtained by suitably relabeling the coordinates. We have also considered conformally related "Einstein frame" to relate the solutions we have obtained with the dilaton-Maxwell type solutions that exist in the literature. We see that for a special case the general solution we present reduces to Dilaton-Melvin spacetime. The General Relativistic limit of these solutions are also discussed and we found that this limit is different from the four dimensional case.