  Using minimalist assumptions we develop a natural functional decomposition
for the spacetime metric, and explicit tractable formulae for the surface
gravities, in arbitrary stationary circular (PT symmetric) axisymmetric
spacetimes. We relate rigidity results, (the existence of a Killing horizon),
and the zeroth law to the absence of curvature singularities at the would-be
horizons. These observations are of interest to both observational
astrophysicists (modelling the cold, dark, heavy objects at the centre of most
spiral galaxies), and to the analogue spacetime community, (wherein the
presence of naked singularities is not necessarily deprecated, and the
occurrence of non-Killing horizons is relatively common).
