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In General Relativity, it is assumed that the metric can LOCALLY, be always transformed to a metric with Lorentzian signature: $(+,-,-,-)$. Given a certain metric at a certain space point - What does the transformation, which transforms the metric at that point to a flat metric, tell us? What conclusions can one draw from the transformation about that point in space time?

eeqesri
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    This is false. General Relativity admits no such assumption. Otherwise, he Riemann tensor which measures geodesic deviation could be transformed away. Perhaps you are thinking of the fact that we can always choose coordinates at any point such that the metric is Lorentzian there? Cheers! – Robert Lewis Jun 17 '17 at 16:32
  • Oh yea. That's true. That is what I meant. – eeqesri Jun 17 '17 at 17:07
  • You might consider editing your question to be more accurately stated. Or perhaps I will . . . It'll be a nice question once the errors are fixed! Cheers! – Robert Lewis Jun 17 '17 at 17:09

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