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Uniqueness Results for Ill-Posed Characteristic Problems in Curved Space-Times

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Abstract

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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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin – Madison, Madison, WI, 53706, USA

    Alexandru D. Ionescu

  2. Department of Mathematics, Fine Hall, Princeton University, Princeton, NJ, 08544, USA

    Sergiu Klainerman

Authors
  1. Alexandru D. Ionescu
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  2. Sergiu Klainerman
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Correspondence to Sergiu Klainerman.

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Communicated by P. Constantin

The first author was supported in part by an NSF grant and a Packard Fellowship.

The second author was supported by NSF grant DMS 0070696.

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Ionescu, A.D., Klainerman, S. Uniqueness Results for Ill-Posed Characteristic Problems in Curved Space-Times. Commun. Math. Phys. 285, 873–900 (2009). https://doi.org/10.1007/s00220-008-0650-y

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  • DOI: https://doi.org/10.1007/s00220-008-0650-y

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