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

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 Kr...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2022-03, Vol.82 (3), p.1-20, Article 215
Main Authors: Fröb, Markus B., Khavkine, Igor, Málek, Tomáš, Pravda, Vojtěch
Format: Article
Language:English
Subjects:
Algebra
Analysis
Astronomy
Astrophysics and Cosmology
Black holes
Boundary value problems
Coordinates
Electromagnetism
Elementary Particles
Gravitational waves
Gravity
Hadrons
Heavy Ions
Horizon
Mathematical analysis
Maxwell's equations
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Rotation
String Theory
Tensors
Well posed problems
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Summary: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.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-022-10160-z