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General Relativity with Torsion - Slimy.com
General Relativitywith Torsion :Extending Wald s Chapter on CurvatureSteuard Jensen Enrico Fermi Institute and Department of PhysicsUniversity of Chicago5640 S. Ellis Avenue, Chicago IL 60637, USAN ovember 16, 2005 AbstractMost applications of differential geometry, including General rela-tivity, assume that the connection is Torsion free : that vectors donot rotate during parallel transport. Because some extensions of GR(such as string theory) do include Torsion , it is useful to see how torsionappears in standard geometrical definitions and formulas in modernlanguage. In this review article, I step through chapter 3, Curva-ture , of Robert Wald s textbookGeneral Relativityand show whatchanges when the Torsion -free condition is Introduction22 Defining Torsion23 Curvature (with Torsion ) Derivative Operators and Parallel Transport .. Curvature .. Geodesics .. Methods for Computing Curvature .. Coordinate Component Method .. Orthonormal Basis (Tetrad) Methods.
General Relativity with Torsion: Extending Wald’s Chapter on Curvature Steuard Jensen∗ Enrico Fermi Institute and Department of Physics University of Chicago
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