Abstract
Isolated Kerr black holes are thermodynamically stable with respect to axisymmetric perturbations. Holes in a heat bath may be stable with large enough angular momentum. Isolated or not, at a fixed angular velocity divided by the temperature they are all unstable. The stability of the "inner horizons" has also been considered. Isolated inner horizons are stable. With different constraints, they are either stable or unstable. The analysis concerns pure black holes. Thermal radiation around black holes is treated as one of their possible circumstances. The effects of back reaction on the metric and nonconstancy of temperature in a heat bath have been neglected.
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