, Volume 285, Issue 3, pp 873-900

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].

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.