On the existence of simultaneous synchronous coordinates in spacetimes with spacelike singularities

We investigate the issue of when a synchronous coordinate system exists which entirely covers a singularity simultaneously. For a spacetime with a spacelike singularity (or, more precisely, with a spacelike causal boundary) we prove that such coordinates exist if and only if the ’’maximum lifetime function’’ satisfies certain boundedness, differentiability, and limit properties. Our results lend plausibility to the validity of the use of simultaneous synchronous coordinates to analyze physically realistic spacelike singularities. Nevertheless, we construct a number of examples which do not satisfy our conditions and thus do not admit such coordinates.