I understand that one can always construct a set Synchronous coordinates (or Gaussian normal coordinates) on a neighborhood of a point in spacetime.(adsbygoogle = window.adsbygoogle || []).push({});

My question is:

Does one can construct a metric with only $g_{0i}=0$ such that

$dS^2=g_{00}dt^2 + g_{ij}dx^{i} dx^{j}$ (where $i=1,,,,D$ and $j=1,,,,D$) not just in a neighborhood of a point but to all spacetime in general?

In this case one should use

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# "Semi" Synchronous coordinates

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