Maximal Analytic Extension and Hidden Symmetries of the Dipole Black Ring
arXiv:1011.5618 · doi:10.1088/0264-9381/28/23/235014
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-Nordström 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.
v1: 36 pages, 2 figures. v2: minor corrections, typos fixed, submitted to Class. Quant. Grav