We can imagine an arbritrary function describing our vector field:
Let's consider a vector field V (x,y, z) representing air moving in a room. In many applications, it is important to know how a vector fiels changes as we move from one location to another.įor vectors expressed using Cartesian coordinates, taking the derivative of a vector is quite staightforward: we simply take the derivative of each of the vector's component. It's important for us to understand what Christoffel symbols do exacly mean from a physical point of view, as we know that in General Relativity, the paths of particles and light beams in free fall are calculated by solving the geodesic equations in which the Christoffel symbols explicitly appear (refer to Geodesic equation and Christoffel symbols)
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