{"paper":{"title":"Linearization stability results and active measurements for the Einstein-scalar field equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Gunther Uhlmann, Matti Lassas, Yaroslav Kurylev","submitted_at":"2014-05-14T07:12:33Z","abstract_excerpt":"We study the Einstein equations coupled with the scalar field equations, $\\hbox{Ein}(g)=T$, $T=T(g,\\phi)+F^1$, and $\\square_g\\phi^\\ell-m^2\\phi^\\ell= F^2$, where the sources $F=(F^1, F^2)$ correspond to perturbations of the physical fields which we control. Here $\\phi=(\\phi^\\ell)_{\\ell=1}^L$ and $(M,g)$ is a 4-dimensional globally hyperbolic Lorentzian manifold. The sources $F$ need to be such that the fields $(g,\\phi,F)$ satisfy the conservation law $\\hbox{div}_g(T)=0$. If $(g_\\epsilon,\\phi_\\epsilon)$ solves the above equations, $\\dot g=\\partial_\\epsilon g_\\epsilon|_{\\epsilon=0}$, $\\dot\\phi=\\p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3384","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"}