Submissions from E. M. Penrose
-  faKiv:2009.08525 [pdf]
The Penrose-Papapetrou equation on the space-time of the Schwarzschild black holeComments: 63 pages, 5 figures; v2: minor corrections, references added; v3: references updated, v4: minor corrections, references added; v5: minor corrections, references updated, v6: minor corrections, references updated
We derive a new and exact formula for the Penrose-Papapetrou equation on the space-time of the Schwarzschild black hole by integrating out the non-perturbative corrections. This is done by taking the Finite Element of the angle of the black hole and evaluating the Penrose-Papapetrou equation. We find exactly the same formula as has been shown by Milner-Fisher, but for the black hole radius, which we find to be precisely the same as the one derived by Milner-Fisher.