= Time-dependent lapse can disguise flat spacetime
{title2=$ds^2=-N(t)^2dt^2+dx^2,\quad T=\int N(t)\,dt$}
For positive lapse $N$, this time reparametrization gives a local <Minkowski metric>. If the new time coordinate ranges over the entire real line, it is a global isometry to Minkowski space. In particular $N=\cosh t$ gives $T=\sinh t$ and complete nonperiodic timelike geodesics. A lapse depending on the spatial coordinate instead can describe a different curved geometry; exchanging the arguments is not a harmless relabeling of the same metric.
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