On the stability of non-supersymmetric supergravity solutions

We examine the stability of some non-supersymmetric supergravity solutions that have been found recently. The first solution is AdS5×M6, for M6 an stretched CP3. We consider breathing and squashing mode deformations of the metric, and find that the solution is stable against small fluctuations of this kind. Next we consider type IIB solution of AdS2×M8, where the compact space is a U(1) bundle over N(1,1). We study its stability under the deformation of M8 and the 5-form flux. In this case we also find that the solution is stable under small fluctuation modes of the corresponding deformations.