On double-black hole solutions of the Einstein-Maxwell-Dilaton theory in five dimensions

TL;DR

This paper introduces a solution-generating method to derive five-dimensional Einstein-Maxwell-Dilaton solutions from four or five-dimensional static charged solutions, illustrating it with dilatonic Reissner-Nordström and double black hole solutions.

Contribution

A novel technique to generate five-dimensional Einstein-Maxwell-Dilaton solutions from lower-dimensional static charged solutions, including analysis of conical singularities and charge-mass relations.

Findings

The dilaton coupling affects conical singularities between black holes.

Proportional charges and masses cancel dilaton effects on singularities.

Constructed explicit dilatonic Reissner-Nordström and double black hole solutions.

Abstract

We describe a solution-generating technique that will map a static charged solution of the Einstein-Maxwell theory in four (or five) dimensions to a five-dimensional solution of the Einstein-Maxwell-Dilaton theory. As examples of this technique first we show first how to construct the dilatonic version of the Reissner-Nordstr\"om solution in five dimensions and then we consider the more general case of the double black hole solutions and describe some of their properties. We found that in the general case the value of the conical singularities in between the black holes is affected by the dilaton's coupling constant to the gauge field and only in the particular case when all charges are proportional to the masses this dependence cancels out.