TY - JOUR

T1 - Rigidity of stationary black holes with small angular momentum on the horizon

AU - Alexakis, S.

AU - Ionescu, A. D.

AU - Klainerman, S.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - 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 andWald 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.

AB - 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 andWald 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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U2 - 10.1215/00127094-2819517

DO - 10.1215/00127094-2819517

M3 - Article

AN - SCOPUS:84920090917

VL - 163

SP - 2603

EP - 2615

JO - Duke Mathematical Journal

JF - Duke Mathematical Journal

SN - 0012-7094

IS - 14

ER -