We are stating with equivalence principle that passing locally to non inertial frame would be analogous to the presence of gravitational field at that point, so [itex] g^'_{ij}=A g_{nm} A^{-1} [/itex] where g' is the galilean metric and g is the metric in curved space, and A is the transformation which eliminates gravity at the point.(adsbygoogle = window.adsbygoogle || []).push({});

How do you prove that det[g] <0?

Doesn't it follow from the above realtion that det[g] is exactly -2 because det[g'] = -2, and not just simply negative? What did I miss?

Thanks!

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# Determinant of the metric tensor

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