  We derive constraints on the form of the renormalized stress tensor for
states on Kerr space-time based on general physical principles: symmetry, the
conservation equations, the trace anomaly and regularity on (sections of) the
event horizon. This is then applied to the physical vacua of interest. We
introduce the concept of past and future Boulware vacua and discuss the
non-existence of a state empty at both scri- and scri+. By calculating the
stress tensor for the Unruh vacuum at the event horizon and at infinity, we are
able to check our earlier conditions. We also discuss the difficulties of
defining a state equivalent to the Hartle-Hawking vacuum and comment on the
properties of two candidates for this state.
