Maximal Analytic Extension and Hidden Symmetries of the Dipole Black Ring

TL;DR

This paper constructs analytic extensions of dipole black rings, revealing their causal structures and hidden symmetries, and compares them to Reissner-Nordström black holes, highlighting new geometric and physical insights.

Contribution

It provides the first detailed analytic extensions of dipole black rings and uncovers their hidden symmetries through conformal Killing tensors and related geometric structures.

Findings

Extensions are non-globally hyperbolic with multiple asymptotic regions.

Causal structure resembles that of Reissner-Nordström black holes.

Existence of conformal Killing-Yano tensors indicates hidden symmetries.

Abstract

We construct analytic extensions across the Killing horizons of non-extremal and extremal dipole black rings in Einstein-Maxwell's theory using different methods. We show that these extensions are non-globally hyperbolic, have multiple asymptotically flat regions and in the non-extremal case, are also maximal and timelike complete. Moreover, we find that in both cases the causal structure of the maximally extended space-time resembles that of the 4-dimensional Reissner-Nordstr\"om black hole. Furthermore, motivated by the physical interpretation of one of these extensions, we find a separable solution to the Hamilton-Jacobi equation corresponding to zero energy null geodesics and relate it to the existence of a conformal Killing tensor and a conformal Killing-Yano tensor in a specific dimensionally reduced space-time.