Introduction to tensor calculus for general relativity
Bertschinger E.
There arc three essential ideas underlying general relativity (OR). The first is that space time may be described as a curved, four-dimensional mathematical structure called a pscudo Ricmannian manifold. In brief, time and space together comprise a curved four dimensional non-Euclidean geometry. Consequently, the practitioner of OR must be familiar with the fundamental geometrical properties of curved spacctimc. In particular, the laws of physics must be expressed in a form that is valid independently of any coordinate system used to label points in spacetimc.
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