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Yes, we can, and I did easily by setting ds = 0 in the Schwarzschild solution for a particle described by radially symmetric coordinates with a static metric. The time for transit is governed by a log function of the radius, r, for an observer in the fixed coordinate system and is infinite for him (or her!)

Please someone, kindly explain how this result is consistent with the constancy of the speed of light. The distance to the point at which r = 2m is a determined quantity. If the speed of light does not change, how can the time to traverse it be other than finite for the fixed observer?