Monodromy-Matrix Description of Doubly Rotating Black Rings

TL;DR

This paper develops a monodromy-matrix method to generate and reconstruct doubly rotating black hole solutions in five-dimensional vacuum Einstein theory, extending previous single-angular-momentum analyses.

Contribution

It introduces a solution-generating technique based on the Breitenlohner-Maison linear system for bi-axisymmetric black holes with two angular momenta.

Findings

Constructed the monodromy matrix for doubly rotating Myers-Perry black holes.

Reconstructed black ring solutions via Riemann-Hilbert problem factorization.

Validated the method by reproducing known black hole geometries.

Abstract

Extending the single-angular-momentum case analyzed in our previous work, we investigate the solution-generating technique based on the Breitenlohner-Maison (BM) linear system for asymptotically flat, stationary, bi-axisymmetric black hole solutions with two angular momenta in five-dimensional vacuum Einstein theory. In particular, we construct the monodromy matrix associated with the BM linear system for the doubly rotating Myers-Perry black holes and the Pomeransky-Sen'kov black rings. Conversely, by solving the corresponding Riemann-Hilbert problem using the procedure developed by Katsimpouri et al., we demonstrate that the factorization of the monodromy matrix precisely reproduces these vacuum solutions, thereby reconstructing both geometries.