We devote this chapter to the development of four-dimensional geometry in arbitrary curvilinear coordinates. We shall deal with field quantities. A field quantity has the same nature at all points of space. Such a quantity will be disturbed by the curvature.
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References
Dirac PAM (1975) General Theory of Relativity. (John Wiley & Sons, New York)
Landau LD, Lifshitz EM (1975) The Classical Theory of Fields. (Pergamon Press, Oxford UK)
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(2008). Curvilinear Coordinates and General Tensors. In: Gravity, Black Holes, and the Very Early Universe. Springer, New York, NY. https://doi.org/10.1007/978-0-387-73631-0_2
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