Journal
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Volume 329, Issue 3, Pages 859-891Publisher
SPRINGER
DOI: 10.1007/s00220-014-2033-x
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Funding
- NSF [DMS-0943787]
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For any sub-extremal Kerr spacetime with non-zero angular momentum, we find an open family of non-zero masses for which there exist smooth, finite energy, and exponentially growing solutions to the corresponding Klein-Gordon equation. If desired, for any non-zero integer m, an exponentially growing solution can be found with mass arbitrarily close to . In addition to its direct relevance for the stability of Kerr as a solution to the Einstein-Klein-Gordon system, our result provides the first rigorous construction of a superradiant instability. Finally, we note that this linear instability for the Klein-Gordon equation contrasts strongly with recent work establishing linear stability for the wave equation.
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