TY - JOUR

T1 - Uniqueness results for Ill-posed characteristic problems in curved space-times

AU - Ionescu, Alexandru D.

AU - Klainerman, Sergiu

N1 - Copyright:
Copyright 2009 Elsevier B.V., All rights reserved.

PY - 2009/2

Y1 - 2009/2

N2 - We prove two uniqueness theorems concerning linear wave equations; the first theorem is in Minkowski space-times, while the second is in the domain of outer communication of a Kerr black hole. Both theorems concern ill-posed Cauchy problems on bifurcate, characteristic hypersurfaces. In the case of the Kerr space-time, the hypersurface is precisely the event horizon of the black hole. The uniqueness theorem in this case, based on two Carleman estimates, is intimately connected to our strategy to prove uniqueness of the Kerr black holes among smooth, stationary solutions of the Einstein-vacuum equations, as formulated in [14].

AB - We prove two uniqueness theorems concerning linear wave equations; the first theorem is in Minkowski space-times, while the second is in the domain of outer communication of a Kerr black hole. Both theorems concern ill-posed Cauchy problems on bifurcate, characteristic hypersurfaces. In the case of the Kerr space-time, the hypersurface is precisely the event horizon of the black hole. The uniqueness theorem in this case, based on two Carleman estimates, is intimately connected to our strategy to prove uniqueness of the Kerr black holes among smooth, stationary solutions of the Einstein-vacuum equations, as formulated in [14].

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U2 - 10.1007/s00220-008-0650-y

DO - 10.1007/s00220-008-0650-y

M3 - Article

AN - SCOPUS:58149494382

VL - 285

SP - 873

EP - 900

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -