On well-posedness and algebraic type of the five-dimensional charged rotating black hole with two equal-magnitude angular momenta

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.

v2: 26 pages, 1 figure, close to published version

References in corpus (12)

• Rotating Black Holes in Higher Dimensional Einstein-Maxwell Gravity
• Algebraic classification of higher dimensional spacetimes based on null alignment
• Charged Rotating Black Holes in Odd Dimensions
• The Asymptotic Behavior of Massless Fields and the Memory Effect
• Kerr-NUT-de Sitter Curvature in All Dimensions
• Higher dimensional Kerr-Schild spacetimes
• Braneworld black holes
• The asymptotic structure of electromagnetism in higher spacetime dimensions
• Geometric Horizons
• Bel-Debever criteria for the classification of the Weyl tensors in higher dimensions
• Black rings with a small electric charge: gyromagnetic ratios and algebraic alignment
• Asymptotic behaviour of Maxwell fields in higher dimensions

Cited by in corpus (1)

• Charging Kerr-Schild spacetimes in higher dimensions