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The Choice of Riemannian Geometry
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antisymmetric appears approximate arbitrary assume becomes body calculate called Chap Christoffel symbols classical clearly coefficients components condition consider constant coordinate system corresponding covariant curve defined definition density depends derivatives described determine differential differential equations discussed distance easily effect Einstein electromagnetic energy equal expression fact field equations force function geodesic geometry given gives gravitational field identity important independent indices integral interesting interpretation introduce invariant leads light line element linear Lorentz metric mass mathematical matrix matter measured metric tensor motion observer obtain parameter particle particular physical possible potential present problem properties quantity radial radius relation relativity represents result Riemann tensor rotating scalar Schwarzschild shift simple solution solve space special relativity stars surface symmetric theory tion transformation universe variational vector field write written zero