โ Scribed by Steuard Jensen, Robert M. Wald
No coin nor oath required. For personal study only.
This file comes from http://www.slimy.com/~steuard/teaching/tutorials/
Most applications of differential geometry, including general relativity, assume that the connection is โtorsion freeโ: that vectors do not rotate during parallel transport. Because some extensions of GR (such as string theory) do include torsion, it is useful to see how torsion appears in standard geometrical definitions and formulas in modern language. In this review article, I step through chapter 3, โCurvatureโ, of Robert Waldโs textbook General Relativity and show what changes when the torsion-free condition is relaxed.
Introduction
Defining Torsion
Curvature (with Torsion)
Derivative Operators and Parallel Transport
Curvature
Geodesics
Methods for Computing Curvature
Coordinate Component Method
Orthonormal Basis (Tetrad) Methods
B-Fields and Non-symmetric Metrics
Differential Forms, et cetera
Differential Forms
๐ SIMILAR VOLUMES
This file comes from http://physics.drexel.edu/~dcross/papers/wald.pdf Solutions to General Relativity by Wald, Daniel J. Cross
This file comes from https://doku.pub/documents/braune-l-solutions-to-problems-from-walds-general-relativitypdf-nl3vj4k2o8q1 Solutions to Problems from Waldโs Book โGeneral Relativityโ, Lucas Braune, September 29, 2010
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