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    $\begingroup$ Spacetime is covered by a single metric-preserving chart if and only if you are studying special relativity. $\endgroup$ Commented Feb 17, 2019 at 5:25
  • $\begingroup$ Thanks, I understand now, indeed I was carrying stereotypes from special relatively $\endgroup$ Commented Feb 17, 2019 at 5:49
  • $\begingroup$ As an example I found atlas of de sitter space: arxiv.org/abs/1211.2363 $\endgroup$ Commented Feb 17, 2019 at 5:55
  • $\begingroup$ @WillO: Spacetime is covered by a single metric-preserving chart if and only if you are studying special relativity. The part about "metric-preserving" isn't relevant to the OP. $\endgroup$ Commented Feb 17, 2019 at 15:22
  • $\begingroup$ @BenCrowell: I agree that it is not relevant to the question that the OP actually asked, but I am at least 70% confident that it is relevant to the underlying confusion. $\endgroup$ Commented Feb 17, 2019 at 16:38