On the uniqueness of smooth, stationary black holes in vacuum

TY - JOUR

T1 - On the uniqueness of smooth, stationary black holes in vacuum

AU - Ionescu, Alexandru D.

AU - Klainerman, Sergiu

PY - 2009/1

Y1 - 2009/1

N2 - A fundamental conjecture in general relativity asserts that the domain of outer communication of a regular, stationary, four dimensional, vacuum black hole solution is isometrically diffeomorphic to the domain of outer communication of a Kerr black hole. So far the conjecture has been resolved, by combining results of Hawking [17], Carter [4] and Robinson [28], under the additional hypothesis of non-degenerate horizons and real analyticity of the space-time. We develop a new strategy to bypass analyticity based on a tensorial characterization of the Kerr solutions, due to Mars [24], and new geometric Carleman estimates. We prove, under a technical assumption (an identity relating the Ernst potential and the Killing scalar) on the bifurcate sphere of the event horizon, that the domain of outer communication of a smooth, regular, stationary Einstein vacuum spacetime of dimension 4 is locally isometric to the domain of outer communication of a Kerr spacetime.

AB - A fundamental conjecture in general relativity asserts that the domain of outer communication of a regular, stationary, four dimensional, vacuum black hole solution is isometrically diffeomorphic to the domain of outer communication of a Kerr black hole. So far the conjecture has been resolved, by combining results of Hawking [17], Carter [4] and Robinson [28], under the additional hypothesis of non-degenerate horizons and real analyticity of the space-time. We develop a new strategy to bypass analyticity based on a tensorial characterization of the Kerr solutions, due to Mars [24], and new geometric Carleman estimates. We prove, under a technical assumption (an identity relating the Ernst potential and the Killing scalar) on the bifurcate sphere of the event horizon, that the domain of outer communication of a smooth, regular, stationary Einstein vacuum spacetime of dimension 4 is locally isometric to the domain of outer communication of a Kerr spacetime.

UR - https://www.scopus.com/pages/publications/56349100077

UR - https://www.scopus.com/pages/publications/56349100077#tab=citedBy

U2 - 10.1007/s00222-008-0146-6

DO - 10.1007/s00222-008-0146-6

M3 - Article

SN - 0020-9910

VL - 175

SP - 35

EP - 102

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 1

ER -