General Relativity (General Relativity with Torsion: Extending Wald’s Chapter on Curvature)

This file comes from http://www.slimy.com/~steuard/teaching/tutorials/ Most applications of differential geometry, including general relativity, assume that the connection is “torsion free”: 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, “Curvature”, of Robert Wald’s textbook General Relativity and show what changes when the torsion-free condition is relaxed.