Orthogonal black di-ring solution

TL;DR

This paper constructs an exact five-dimensional solution describing two orthogonal black rings with specific parameters, using the inverse scattering method, and introduces a systematic way to generate seed metrics for such solutions.

Contribution

It presents a new exact solution for orthogonal black di-rings and a systematic method to construct seed metrics for multi-black-ring configurations.

Findings

Constructed a five-dimensional orthogonal black di-ring solution.

Developed a systematic method for seed metric construction.

Potential to generate more complex multi-black-ring solutions.

Abstract

We construct a five dimensional exact solution of the orthogonal black di-ring which has two black rings whose $S^1$-rotating planes are orthogonal. This solution has four free parameters which represent radii of and speeds of $S^1$-rotation of the black rings. We use the inverse scattering method. This method needs the seed metric. We also present a systematic method how to construct a seed metric. Using this method, we can probably construct other solutions having many black rings on the two orthogonal planes with or without a black hole at the center.