We present a simple proof, using the conservation equations, that any quant
um stress tensor on Kerr space-time which is isotropic in a frame which rot
ates rigidly with the angular velocity of the event horizon must be diverge
nt at the velocity of light surface. We comment on our result in the light
of the absence of a 'true Hartle-Hawking' vacuum for Kerr. (C) 2000 Elsevie
r Science B.V. All rights reserved.