Completely integrable sector in 5D Einstein-Maxwell gravity and derivation of the dipole black ring solutions

TL;DR

This paper demonstrates the complete integrability of a sector of 5D Einstein-Maxwell gravity with specific symmetries, develops a solution-generating method, and derives a new rotating solution including the dipole black ring.

Contribution

It introduces a Lax-pair formulation for the reduced equations and constructs a new rotating 5D Einstein-Maxwell solution with dipole black ring features.

Findings

Derived a Lax-pair for integrable 2D EM equations.

Developed a solution-generating technique for exact solutions.

Constructed a new six-parameter rotating 5D EM solution including dipole black rings.

Abstract

We consider 5D Einstein-Maxwell (EM) gravity in spacetimes with three commuting Killing vectors: one timelike and two spacelike Killing vectors one of them being hypersurface-orthogonal. Assuming a special ansatz for the Maxwell field we show that the 2-dimensional reduced EM equations are completely integrable by deriving a Lax-pair presentation. We also develop a solution generating method for explicit construction of exact EM solutions with considered symmetries. We also derive explicitly a new rotating six parametric 5D EM solution which includes the dipole black ring solution as a particular case.