On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
arXiv:2112.13266 · doi:10.1140/epjc/s10052-022-10160-z
Abstract
We study various mathematical aspects of the charged rotating black hole with two equal-magnitude angular momenta in five dimensions. We introduce a coordinate system that is regular on the horizon and in which Einstein-Maxwell equations reduce to an autonomous system of ODEs. Employing Bondi and Kruskal-like coordinates, we analyze the geometric regularity of the black hole metric at infinity and the horizon, respectively, and the well-posedness of the corresponding boundary value problem. We also study the algebraic types of the electromagnetic and curvature tensors. While outside the horizon the electromagnetic and Ricci tensors are of type D, the Weyl tensor is algebraically general. The Weyl tensor simplifies to type~II on the horizon and type~D on the bifurcation sphere. These results imply inconsistency of the metric with the Kerr--Schild form with a geodesic Kerr-Schild vector. This feature is shared by the four-dimensional Kerr-Newman metric and the vacuum Myers-Perry or charged Schwarzschild-Tangherlini geometries in arbitrary dimension, but hence not by the black hole we have considered here.
arXiv commentv2: 26 pages, 1 figure, close to published version
References in corpus (28)
- Classification of the Weyl Tensor in Higher Dimensions
- Alignment and algebraically special tensors in Lorentzian geometry
- Asymptotic Flatness and Bondi Energy in Higher Dimensional Gravity
- Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity
- Algebraic classification of higher dimensional spacetimes based on null alignment
- Bianchi identities in higher dimensions
- Five Dimensional Rotating Black Hole in a Uniform Magnetic Field. The Gyromagnetic Ratio
- Charged Rotating Black Holes in Odd Dimensions
- The Asymptotic Behavior of Massless Fields and the Memory Effect
- Five-Dimensional Charged Rotating Black Holes
- Asymptotic flatness at null infinity in arbitrary dimensions
- Quasi-local rotating black holes in higher dimension: geometry
- Higher dimensional Kerr-Schild spacetimes
- Kerr-NUT-de Sitter Curvature in All Dimensions
- Braneworld black holes
- A Slowly Rotating Charged Black Hole in Five Dimensions
- Quasi-Spherical Light Cones of the Kerr Geometry
- The asymptotic structure of electromagnetism in higher spacetime dimensions
- On asymptotic structure at null infinity in five dimensions
- Geometric Horizons
- Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions
- Charged rotating black holes in higher dimensions
- Perturbative Charged Rotating 5D Einstein-Maxwell Black Holes
- Black rings with a small electric charge: gyromagnetic ratios and algebraic alignment
- Asymptotic flatness at spatial infinity in higher dimensions
- Kerr black holes in horizon-generating form
- Asymptotic behaviour of Maxwell fields in higher dimensions
- A note on the Kerr-Newman metric in five dimensions