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].
UR - http://www.scopus.com/inward/record.url?scp=58149494382&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=58149494382&partnerID=8YFLogxK
U2 - 10.1007/s00220-008-0650-y
DO - 10.1007/s00220-008-0650-y
M3 - Article
AN - SCOPUS:58149494382
SN - 0010-3616
VL - 285
SP - 873
EP - 900
JO - Communications In Mathematical Physics
JF - Communications In Mathematical Physics
IS - 3
ER -