Transcription of Introduction to Tensor Calculus for General Relativity
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Introduction to Tensor Calculus for General Relativity
Massachusetts Institute of Technology Department of Physics Physics Spring 1999. Introduction to Tensor Calculus for General Relativity c 1999 Edmund Bertschinger. All rights reserved. 1 Introduction There are three essential ideas underlying General Relativity (GR). The first is that space- time may be described as a curved, four-dimensional mathematical structure called a pseudo-Riemannian manifold. In brief, time and space together comprise a curved four- dimensional non-Euclidean geometry. Consequently, the practitioner of GR must be familiar with the fundamental geometrical properties of curved spacetime.
special relativity. This is Einstein’s famous strong equivalence principle and it makes general relativity an extension of special relativity to a curved spacetime. The third key idea is that mass (as well as mass and momentum flux) curves spacetime in a manner described by the tensor field equations of Einstein.
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