Bonnor-type Black Dihole Solution in Brans-Dicke-Maxwell Theory

TL;DR

This paper constructs and analyzes a Bonnor-type magnetic black dihole solution within Brans-Dicke-Maxwell theory, extending known Einstein-Maxwell solutions and exploring its unique features and stability.

Contribution

It introduces a new black dihole solution in Brans-Dicke-Maxwell theory derived from Einstein-Maxwell solutions using Singh and Rai's algorithm.

Findings

Solution exhibits internal infinity of the symmetry axis

Analysis of the solution's stability issues

Detailed discussion of the solution's peculiar features

Abstract

It was originally thought that Bonnor's solution in Einstein-Maxwell theory describes a singular point-like magnetic dipole. Lately, however, it has been demonstrated that indeed it may describe a black {\it dihole}, i.e., a pair of static, oppositely-charged extremal black holes with regular horizons. Motivated particularly by this new interpretation, in the present work, the construction and extensive analysis of a solution in the context of the Brans-Dicke-Maxwell theory representing a black dihole are attempted. It has been known for some time that the solution-generating algorithm of Singh and Rai produces stationary, axisymmetric, charged solutions in Brans-Dicke-Maxwell theory from the known such solutions in Einstein-Maxwell theory. Thus this algorithm of Singh and Rai's is employed in order to construct a Bonnor-type magnetic black dihole solution in Brans-Dicke-Maxwell theory from the known Bonnor solution in Einstein-Maxwell theory. The peculiar feature of the new solution including internal infinity nature of the symmetry axis and its stability issue have been discussed in full detail.