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Unstable mode solutions to the Klein-Gordon equation in Kerr-anti-de Sitter spacetimes

dc.creatorDold, Dominic
dc.date.accessioned2016-08-17
dc.date.accessioned2018-11-24T23:26:55Z
dc.date.available2016-10-12T12:34:53Z
dc.date.available2018-11-24T23:26:55Z
dc.date.issued2016
dc.identifierhttps://www.repository.cam.ac.uk/handle/1810/260736
dc.identifier.urihttp://repository.aust.edu.ng/xmlui/handle/123456789/3912
dc.description.abstractFor any cosmological constant Λ = −3/$l^2$ < 0 and any $\alpha$ < 9/4, we find a Kerr-AdS spacetime ($M$, $g_{KAdS}$), in which the Klein-Gordon equation $\square g_{KAdS}$ ψ+$\alpha$/$l^2$ψ = 0 has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound r$^{+2}_{−+}$ > |$a$|$l$. We obtain an analogous result for Neumann boundary conditions if 5/4 < $\alpha$ < 9/4. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses $\alpha$ such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result adopts methods of Shlapentokh-Rothman developed in [SR13] and provides the first rigorous construction of a superradiant instability for negative cosmological constant.
dc.languageen
dc.publisherSpringer
dc.publisherCommunications in Mathematical Physics
dc.titleUnstable mode solutions to the Klein-Gordon equation in Kerr-anti-de Sitter spacetimes
dc.typeArticle


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