{"paper":{"title":"Null distance on a spacetime","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc"],"primary_cat":"math.DG","authors_text":"Carlos Vega, Christina Sormani","submitted_at":"2015-08-03T19:00:05Z","abstract_excerpt":"Given a time function $\\tau$ on a spacetime $M$, we define a `null distance function', $\\hat{d}_\\tau$, built from and closely related to the causal structure of $M$. In basic models with timelike $\\nabla \\tau$, we show that 1) $\\hat{d}_\\tau$ is a definite distance function, which induces the manifold topology, 2) the causal structure of $M$ is completely encoded in $\\hat{d}_\\tau$ and $\\tau$. In general, $\\hat{d}_\\tau$ is a conformally invariant pseudometric, which may be indefinite. We give an `anti-Lipschitz' condition on $\\tau$, which ensures that $\\hat{d}_\\tau$ is definite, and show this co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00531","kind":"arxiv","version":2},"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"}