Transcription of Introduction to Tensor Calculus for General Relativity
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Introduction to Tensor Calculus for General Relativity
Massachusetts Institute of TechnologyDepartment of PhysicsPhysics 1999 Introduction to Tensor Calculus for GeneralRelativityc 1999 Edmund Bertschinger. All rights IntroductionThere 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 apseudo-Riemannian manifold. In brief, time and space together comprise a curved four-dimensional non-Euclidean geometry. Consequently, the practitioner of GR must befamiliar with the fundamental geometrical properties of curved spacetime.
geometry, see the introductory texts of Lovelock and Rund 1975, Bishop and Goldberg ... It is sufficient to develop the needed differential geometry as a straightforward extension of linear algebra and vector calculus. However, it is important to keep in mind the geometrical interpretation of physical quantities. For this reason,
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