{"paper":{"title":"Local vs. global temperature under a positive curvature condition","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","math.MP"],"primary_cat":"math-ph","authors_text":"Ko Sanders","submitted_at":"2016-05-03T13:17:51Z","abstract_excerpt":"For a massless free scalar field in a globally hyperbolic space-time we compare the global temperature T, defined for the KMS states $\\omega^T$, with the local temperature $T_{\\omega}(x)$ introduced by Buchholz and Schlemmer. We prove the following claims: (1) Whenever $T_{\\omega^T}(x)$ is defined, it is a continuous, monotonically increasing function of T at every point x. (2) $T_{\\omega}(x)$ is defined when the space-time is ultra-static with compact Cauchy surface and non-trivial scalar curvature $R\\ge 0$, $\\omega$ is stationary and a few other assumptions are satisfied. Our proof of (2) re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.00895","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"}