Ultrastatic space-times

Several calculations in conformally static space-times rely on the introduction of an ultrastatic background. I describe the general properties of ultrastatic space-times, and then focus on the problem of whether a given space-time can be ultrastatic, or conformally ultrastatic, in more than one way. I show that the first possibility arises if and only if the space-time contains regions that are products with a Minkowskian factor, and that the second arises if and only it contains regions whose spatial sections are conformal to a product space.