1995/03/28 by Markus Heusler, M. Heusler · 29 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Event horizon #Extremal black hole #Penrose process #Pulsars and Gravitational Waves Research #Rigidity (electromagnetism) #Ring singularity #Rotating black hole #Spacetime #Uniqueness #gr-qc
paper · pdf · doi:10.1088/0264-9381/12/8/017
published in Classical and Quantum Gravity 12(8), 2021-2035 (IOP Publishing) · 18 pages, latex, no figures
arxiv created 1995/03/28 · openalex publication_date 1995/08/01 · arxiv updated 2010/04/06 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with a regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.