  We show that the pathology which afflicts the Hartle-Hawking vacuum on the
Kerr black hole space-time can be regarded as due to rigid rotation of the
state with the horizon in the sense that when the region outside the
speed-of-light surface is removed by introducing a mirror, there is a state
with the defining features of the Hartle-Hawking vacuum. In addition, we show
that when the field is in this state, the expectation value of the
energy-momentum stress tensor measured by an observer close to the horizon and
rigidly rotating with it corresponds to that of a thermal distribution at the
Hawking temperature rigidly rotating with the horizon.
