  We study black holes in AdS-like spacetimes, with the horizon given by an
arbitrary positive curvature Einstein metric. A criterion for classical
instability of such black holes is found in the large and small black hole
limits. Examples of large unstable black holes have a B\"ohm metric as the
horizon. These, classically unstable, large black holes are locally
thermodynamically stable. The gravitational instability has a dual description,
for example by using the $AdS_7 \times S^4$ version of the AdS/CFT
correspondence. The instability corresponds to a critical temperature of the
dual thermal field theory defined on a curved background.
