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We study the properties of a modified version of the Bona-Masso family ofhyperbolic slicing conditions. This modified slicing condition has two veryimportant features: In the first place, it guarantees that if a spacetime isstatic or stationary, and one starts the evolution in a coordinate system inwhich the metric coefficients are already time independent, then they willremain time independent during the subsequent evolution, {\em i.e.} the lapsewill not evolve and will therefore not drive the time lines away from theKilling direction. Second, the modified condition is naturally adapted to theuse of a densitized lapse as a fundamental variable, which in turn makes it agood candidate for a dynamic slicing condition that can be used in conjunctionwith some recently proposed hyperbolic reformulations of the Einstein evolutionequations.Comment: 11 page

A hyperbolic slicing condition adapted to Killing fields and densitized lapses