2018/11/16 by Levi Lopes de Lima, Frederico Girão, Amilcar Montalbán
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Boundary (topology) #Boundary value problem #Einstein #Einstein tensor #Geometric Analysis and Curvature Flows #Limiting #Manifold (fluid mechanics) #Metric (unit) #Nonlinear Partial Differential Equations #Tensor (intrinsic definition) #gr-qc #math.DG
paper · pdf · doi:10.1088/1361-6382/ab090a
11 pages; no figures
arxiv created 2018/11/16 · openalex created_date 2018/11/29 · openalex publication_date 2019/02/21 · arxiv updated 2019/03/27 · openalex updated_date 2026/08/05
Abstract It is shown that the mass of an asymptotically flat manifold with a noncompact boundary can be computed in terms of limiting surface integrals involving the Einstein tensor of the interior metric and the Newton tensor attached to the second fundamental form of the boundary. This extends to this setting previous results by several authors in the boundaryless case. The method outlined below, which is based on a coordinate-free approach due to Herzlich, also applies to asymptotically hyperbolic manifolds, again with a noncompact boundary, for which a similar notion of mass has been recently considered by Almaraz and the first named author, and both cases will be discussed here.