Let \(\vec{e}_{\hat{0}}\) be the 4-velocity field (\(x^0=ct, c=1, x^0=t\)) of the reference particles in a reference frame R. We are going to find the metric tensor \(\gamma_{ij}\) in a tangent space orthogonal to \(\vec{e}_{\hat{0}}\), expressed by the metric tensor \(g_{\mu\nu}\) of spacetime.
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Grøn, Ø. (2009). Accelerated Reference Frames. In: Lecture Notes on the General Theory of Relativity. Lecture Notes in Physics, vol 772. Springer, New York, NY. https://doi.org/10.1007/978-0-387-88134-8_4
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DOI: https://doi.org/10.1007/978-0-387-88134-8_4
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