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

Stoytcho S. Yazadjiev
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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.

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Stoytcho S. Yazadjiev. 2006-04-18. Completely integrable sector in 5D Einstein-Maxwell gravity and derivation of the dipole black ring solutions. https://doi.org/10.1103/physrevd.73.104007

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