Basic postulate of GR is that locally spacetime looks flat i.e. any metric can be reduced to a local inertial metric at a point. The local inertial metric is exactly the flat Minkowski metric AT the point, and has zero derivatives AT the point but those are not true away from the point.(adsbygoogle = window.adsbygoogle || []).push({});

Then Newtonian metric is the metric felt by a free fall observer. In it, the deviations from the Minkowski metric, to first order in 1/c^2, are described by a 'Newtonian gravitational potential'. I think this is the same thing as writing a general metric in 'Newtonian approximation', 'Newtonian gauge' or 'Weak field approximation'.

I have a general metric and need a Mathematica notebook that will convert it to the Newtonian metric felt by a specified free fall observer. Does anyone know of something like that ?

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# Mathematica notebook for conversion to newtonian metric ?

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