![]() Source wikipedia 2-surface Gaussian curvature We recall that the geodesic equation for a particule with mass isĪs we know that in General Relativity gravity is equivalent to spacetime curvature, can we then affirm that if all the Christoffel symbols are null, then spacetime is flat, as we have verified in our article Geodesic exercise part I: calculation for 2-dimensional Euclidean space for a two-dimensional Euclidean space - in which geodesics are straight lines? Surfaces with different signed Gaussian curvatures ![]() ![]() But we have to understand in more details how these two concepts are related. So far we have seen how free particles move in spacetime, and it led us to the concept of geodesic. ![]()
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