Einstein Relatively Easy

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If m is any point in the Riemannian manifold M, then there exists a local coordinate system at m such that:


We call such a coordinate system a local inertial frame or a normal frame.

 Corollary: As all the first order derivatives of the metric are null, given the Christoffel symbol expression:

then in a local inertial referential  the vanishing of the partial derivatives of the metric tensor at any point of M is equivalent to the vanishing of Christoffel symbols at that point and in this referential the geodesics are straight lines.



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"Five or six weeks elapsed between the conception of the idea for the special theory of relativity and the completion of the relevant publication" Einstein to Carl Seeling on March 11, 1952

"Every boy in the streets of Göttingen understands more about four-dimensional geometry than Einstein. Yet, in spite of that, Einstein did the work and not the mathematicians."
David Hilbert

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