Black diholes in five dimensions

TL;DR

This paper develops a method to generate five-dimensional black dihole solutions in dilaton gravity, revealing new static configurations of extremal magnetic black holes with various charge arrangements and external magnetic fields.

Contribution

It introduces a generalized Weyl formalism to construct novel five-dimensional black dihole solutions with different charge and background field configurations.

Findings

Constructed static extremal magnetic black hole pairs in five dimensions.

Demonstrated equilibrium maintained by conical singularities.

Presented solutions with background magnetic fields and unbalanced charges.

Abstract

Using a generalized Weyl formalism, we show how stationary, axisymmetric solutions of the four-dimensional vacuum Einstein equation can be turned into static, axisymmetric solutions of five-dimensional dilaton gravity coupled to a two-form gauge field. This procedure is then used to obtain new solutions of the latter theory describing pairs of extremal magnetic black holes with opposite charges, known as black diholes. These diholes are kept in static equilibrium by membrane-like conical singularities stretching along two different directions. We also present solutions describing diholes suspended in a background magnetic field, and with unbalanced charges.