{"paper":{"title":"Refocusing of Light Rays in Space-Time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"math.GT","authors_text":"Paul Kinlaw","submitted_at":"2010-05-14T18:07:27Z","abstract_excerpt":"We investigate refocusing and strong refocusing of light rays in a space-time.  A strongly refocusing space-time is refocusing.  The converse is unknown.  We construct examples of space-times which are refocusing, but not strongly so, at a particular point.  These space-times are strongly refocusing at other points.  The geometrization conjecture proved by Perelman implies that a globally hyperbolic refocusing space-time of dimension $\\leq 4$ admits a strongly refocusing Lorentz metric. \n We show that the possibly empty set of points at which a strongly causal space-time is refocusing is close"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1005.2591","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}