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 AdS_5 X M_6, for M_6 an stretched CP^3. 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 AdS_2 X M_8, where the compact space is a U(1) bundle over N(1,1). We study its stability under the deformation of M_8 and the 5-form flux. In this case we also find that the solution is stable under small fluctuation modes of the corresponding deformations.