Differential geometry MOC

Spherical coördinates in differential geometry

Convention

This Zettel uses the Physics convention

The standard global coördinate chart for is given by the identity map. We call these coördinates . Spherical coördinates are better suited to situations with spherical symmetry. Let . The coördinate chart is defined so that

The metric is

so we see the coördinate basis is orthogonal but not orthonormal. Thus we can adjust to get a vielbein

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