Unbalanced Pomeransky-Sen'kov black ring

TL;DR

This paper generalizes the known balanced doubly rotating black ring solution to an unbalanced case with conical singularities, providing a more compact form and detailed derivation using inverse-scattering, while exploring its properties and limits.

Contribution

The paper introduces a more compact unbalanced Pomeransky-Sen'kov black ring solution derived via inverse-scattering, extending previous models to include conical singularities.

Findings

Derived a new unbalanced black ring solution with conical singularities

Showed how to recover known limits from the new solution

Provided detailed derivation using inverse-scattering method

Abstract

The Pomeransky-Sen'kov solution is well known to describe an asymptotically flat doubly rotating black ring in five dimensions, whose self-gravity is exactly balanced by the centrifugal force arising from the rotation in the ring direction. In this paper, we generalise this solution to the unbalanced case, in which there is in general a conical singularity in the space-time. Unlike a previous form of this solution presented in the literature, our form is much more compact. We describe in detail how this solution can be derived using the inverse-scattering method, and study its various properties. In particular, we show how various known limits can be recovered as special cases of this solution.