merav
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I understand that one can always construct a set Synchronous coordinates (or Gaussian normal coordinates) on a neighborhood of a point in spacetime.
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
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