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1 November 2014 Rigidity of stationary black holes with small angular momentum on the horizon
S. Alexakis, A. D. Ionescu, S. Klainerman
Duke Math. J. 163(14): 2603-2615 (1 November 2014). DOI: 10.1215/00127094-2819517


We prove a black hole rigidity result for slowly rotating stationary solutions of the Einstein vacuum equations. More precisely, we prove that the domain of outer communications of a regular stationary vacuum is isometric to the domain of outer communications of a Kerr solution, provided that the stationary Killing vector-field T is small (depending only on suitable regularity properties of the black hole) on the bifurcation sphere. No other global restrictions are necessary.

The proof brings together ideas from our previous work with ideas from the classical work of Sudarsky and Wald on the staticity of stationary black hole solutions with zero angular momentum on the horizon. It is thus the first uniqueness result, in the framework of smooth, asymptotically flat, stationary solutions, which combines local considerations near the horizon, via Carleman estimates, with information obtained by global elliptic estimates.


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S. Alexakis. A. D. Ionescu. S. Klainerman. "Rigidity of stationary black holes with small angular momentum on the horizon." Duke Math. J. 163 (14) 2603 - 2615, 1 November 2014.


Published: 1 November 2014
First available in Project Euclid: 31 October 2014

zbMATH: 1311.35309
MathSciNet: MR3273578
Digital Object Identifier: 10.1215/00127094-2819517

Primary: 35L72
Secondary: 53Z05

Keywords: black holes , Einstein , rigidity

Rights: Copyright © 2014 Duke University Press


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Vol.163 • No. 14 • 1 November 2014
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