Limites de massas quasi-locais de esferas em variedades Riemannianas

• Autor(a) principal: Nunes, Thays Ingrid dos Santos
• Data de Publicação: 2022
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Biblioteca Digital de Teses e Dissertações da UFPB
• Texto Completo: https://repositorio.ufpb.br/jspui/handle/123456789/27534
• topic: Matemática; Massa ADM; Massa de Brown-York; Coordenadas normais; Teorema da massa positiva; Mathematics; ADM mass; Brown-York mass; Normal coordinates; Positive mass theorem; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA

In this work, we approach some concepts related to Mathematical Relativity, in order to discuss results related to quasi-local mass limits of spheres in three-dimensional Riemannian manifolds, in the light of the article entitled \Large-sphere and smallsphere limits of the Brown-York mass" by authors X.-Q. Fan, Y. Shi and L.-F. Tam. Initially, we studied and used decay properties of some geometric objects in an asymptotically at three-dimensional manifold in order to study the limit of the quasi-local Brown-York mass in coordinate spheres with su ciently large radius, concluding that this limit converges, in the in nite, for the Arnowitt-Deser-Misner (ADM) mass of the asymptotically at manifold in question. Subsequently, we studied expansions in normal coordinates of geometric structures in order to study the Brown-York mass for geodesic spheres with su ciently small radius, using these results to present quasi-local mass expansions, as well as the behavior of certain spherical volumes. We also study results of the same character for the quasi-local Hawking and isoperimetric masses, in addition to approaching applications of these expansions in the face of the positive mass theorem.