= Lecture Notes on General Relativity by Sean M. Carroll
{c}
{tag=Work by Sean M. Carroll}
{title2=1997}
Author's graduate lecture notes, arXiv:gr-qc/9712019, 1997. Section 2 develops <tangent vectors>, <covectors> and the failure of ordinary <tensor> derivatives under nonlinear coordinate changes; section 3 constructs covariant differentiation, <parallel transport> and <curvature>. Metric and <curvature> signs must be translated when combining conventions.
https://arxiv.org/abs/gr-qc/9712019
https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll2.html[Section 2, Manifolds]
https://ned.ipac.caltech.edu/level5/March01/Carroll3/Carroll3.html[Section 3, Curvature]
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