Boundary Value Problem for Black Rings

TL;DR

This paper proves that under certain symmetry and topological assumptions, the only regular asymptotically flat black ring solution in five-dimensional vacuum Einstein equations is the known Pomeransky-Sen'kov black ring.

Contribution

It establishes a uniqueness theorem for black ring solutions with specified symmetries and horizon topology in five-dimensional vacuum gravity.

Findings

Uniqueness of the Pomeransky-Sen'kov black ring under given conditions

No other regular asymptotically flat black ring solutions exist with these symmetries

Supports the classification of higher-dimensional black hole solutions

Abstract

We study the boundary value problem for asymptotically flat stationary black ring solutions to the five-dimensional vacuum Einstein equations. Assuming the existence of two additional commuting axial Killing vector fields and the horizon topology of $S^1\times S^2$, we show that the only asymptotically flat black ring solution with a regular horizon is the Pomeransky-Sen'kov black ring solution.