  We consider quantum fields around uniformly accelerated black holes. At a
particular value of the acceleration, the Bogolubov transformation which would
be responsible for the late-time Hawking radiation, is found to be trivial.
When this happens, Hawking's thermal radiation, Doppler-shifted or not, is
absent to the asymptotic inertial observers despite the nonzero Hawking
temperature, while the co-moving observers find the black hole radiance exactly
balanced by the acceleration heat bath. After a brief comparison to the
classical system of a uniformly accelerated charge, we close with two important
comments. (Phys. Rev. Lett. 75 (1995) 382)
