  It is (or should be) well known that specification of a heat bath requires
both a temperature and a 4-velocity, the rest frame of the heat bath. In static
spacetimes there is a very natural and unique candidate for the 4-velocity of
the heat bath, the normalized timelike Killing vector. However in stationary
non-static spacetimes the situation is considerably more subtle, and several
different "natural" 4-velocity fields suitable for characterizing the rest
frame of a heat bath can be defined - thus Buchdahl's 1949 analysis for the
Tolman temperature gradient in a stationary spacetime is only part of the
story. In particular, the heat bath most suitable for describing the Hawking
radiation from a rotating black hole is best described in terms of a gradient
flow normal to the spacelike hypersurfaces, not in terms of Killing vectors.
