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

This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by Springer.For any cosmological constant Λ = −3/$l^2$ |$a$|$l$. 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.Engineering and Physical Sciences Research Council, Cambridge Trust, Studienstiftung des deutschen Volke