Speaker
Description
We analyze the semiclassical stability of the Schwarzschild AdS black hole
in the Euclidean partition function approach. We perform this computation
in the large D limit and focus on scalar perturbations. We obtain the equa-
tions for non-spherically symmetric scalar perturbations in a simple form.
For a class of perturbations stability is demonstrated by the S-deformation
method. For some other classes we rule out unstable modes of O(D^2). We
also analyze the spherically symmetric perturbations and demonstrate the
appearance of an unstable mode for small black holes in the large D limit.
We obtain an expression for the eigenvalue corresponding to the unstable
mode to next to leading order in a 1/D expansion. This result agrees with
a previously obtained numerical bound on this eigenvalue. For cosmological
constant zero, our answer matches a previous result obtained for the corre-
sponding eigenvalue for the D dimensional Schwarzschild-Tangherlini black
hole to next to leading order in a 1/D expansion.