## Instabilities in asymptotically AdS spacetimes

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## Abstract

In recent years, more and more efforts have been expended on the study of

In the first part, we are concerned with a superradiant instability for

In the second part, we study perturbations of five-dimensional Eguchi-Hanson-AdS spacetimes exhibiting biaxial Bianchi IX symmetry. Within this symmetry class, the Einstein vacuum equations are equivalent to a system of non-linear partial differential equations for the radius