Regular Article - Theoretical Physics
On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta
Institut für Theoretische Physik, Universität Leipzig, Brüderstraße 16, 04103, Leipzig, Germany
2 Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Prague 1, Czechia
3 Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75, Prague 8, Czechia
Accepted: 18 February 2022
Published online: 10 March 2022
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.
© The Author(s) 2022
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