Solitonic generation of stationary and axisymmetric solutions of five-dimensional general relativity

We describe a solitonic solution-generating technique for the five-dimensional general relativity. Reducing the five-dimensional problem to the four-dimensional one, we can systematically obtain single-rotational axially symmetric vacuum solutions. Applying the technique for some seed solutions, we previously obtained S2-rotating and S1-rotating black ring solutions. The seed solution of S2-rotating black ring is a Minkowski flat spacetime and the one of S1ring is an Euclidean C-metric. We show that the S1-rotating black rings can be superposed by the solution generating technique. We analyze the black di-ring solution for the simplest case of multiple rings. The conical singularity of black di-ring can be cured by the suitable choice of physical parameters