  A general framework is developed to investigate the properties of useful
choices of stationary spacelike slicings of stationary spacetimes whose
congruences of timelike orthogonal trajectories are interpreted as the world
lines of an associated family of observers, the kinematical properties of which
in turn may be used to geometrically characterize the original slicings. On the
other hand properties of the slicings themselves can directly characterize
their utility motivated instead by other considerations like the initial value
and evolution problems in the 3-plus-1 approach to general relativity. An
attempt is made to categorize the various slicing conditions or "time gauges"
used in the literature for the most familiar stationary spacetimes: black holes
and their flat spacetime limit.
