  We consider the stability of black holes within both classical general
relativity and the semiclassical thermodynamic description. In particular, we
study linearised perturbations and their contribution to the gravitational
partition function, addressing technical issues for charged
(Reissner-Nordstrom) and rotating (Kerr-AdS) black holes. Exploring the
connection between classical and thermodynamic stability, we find classical
instabilities of Myers-Perry black holes and bifurcations to new black hole
families.
