Solution generating in 5D Einstein-Maxwell-dilaton gravity and derivation of dipole black ring solutions

TL;DR

This paper develops a method to generate exact solutions in 5D Einstein-Maxwell-dilaton gravity with specific symmetries and explicitly derives rotating dipole black ring solutions, advancing the understanding of higher-dimensional black objects.

Contribution

It introduces a solution generating technique for 5D EMd gravity and explicitly constructs rotating dipole black ring solutions.

Findings

The reduced EMd equations are completely integrable under certain conditions.

A new solution generating method for 5D EMd solutions is developed.

Explicit rotating dipole black ring solutions are derived.

Abstract

We consider 5D Einstein-Maxwell-dilaton (EMd) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors, one of which is hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EMd equations are completely integrable. We also develop a solution generating method for explicit construction of exact EMd solutions from known exact solutions of 5D vacuum Einstein equations with considered symmetries. We derive explicitly the rotating dipole black ring solutions as a particular application of the solution generating method.