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Differentiating the four-velocity contracted with itself
Let us denote $u^\mu$ as the contravarient component of a four velocity at a point in some coordinate system for a pseudo-Riemannian manifold. I want to examine the following equation.
$$\partial_\nu(...
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Conceptual confusion about the formula for parallel transport
I am examining the covariant derivative of a vector according to the formula $$\nabla_{\mu}V^{\nu} = \partial_{\mu}V^{\nu} + \Gamma^{\nu}_{\mu \lambda}V^{\lambda}$$ and also operating under the ...
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