As I recall, in response to my question about which pair of vectors in the tangent space one must use to solve Einstein's Field Equation (since the MT is a linear function of two vectors in the tangent space, and the set of such pairs is infinite and possibly uncountable), you claimed any two vectors along some path is sufficient. But that assumes we know which path we're solving for. What if we want to determine the possible geodesics given some distribution of mass and energy? In general, according to experts, we must first determine the Metric Tensor in that region of space. But generally speaking, how is this done? TY, AG
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