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Explore a rigorous proof demonstrating that non-degenerate smooth compact totally geodesic horizons possess a smooth tangent vector field with constant non-zero surface gravity under the dominant energy condition. Delve into the argument that achronal non-degenerate horizons are Cauchy horizons bounded by chronology-violating regions. Examine the connection between this result and the Isenberg-Moncrief rigidity conjecture, which stems from Penrose's strong cosmic censorship conjecture. Gain insights into advanced concepts in general relativity and horizon physics through this 50-minute lecture presented by Ettore Minguzzi at the BIMSA conference.
