In General Relativity the metric corresponding to an infinitely long massive rod is flat but with a deficit angle. It exhibits a very large deviation from Newtonian gravity in all regions of space in that the effective gravitational potential is flat rather than logarithmic.
My question is is there still a large deviation from Newtonian gravity for finite rods? Specifically if I were near a very long rod would I experience any gravity and/or would I see a deficit angle? Generally physicists are comfortable approximating long rods as infinite but I know that Tipler cylinders only give closed timelike curves if they are actually infinitely long, so there are cases where approximating long rods as infinite fails entirely.
Also if long massive rod don't attract very strongly would you be able to test for deviations from standard GR (such as f(R) gravity) by measuring gravitational force near a long rod?
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