2006/06/30 by Piotr T. Chruściel, Piotr T. Chrusciel, Daniel Maerten +1 · 4 citations
Mathematics · Physics and Astronomy · #Angular momentum #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #De Sitter space #De Sitter universe #Geometric Analysis and Curvature Flows #Hamiltonian (control theory) #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum mechanics #Space (punctuation) #Universe #Upper and lower bounds #gr-qc #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/11/084
published as JHEP 0611 (2006) 084 · improvements in the presentation; some statements corrected
arxiv created 2006/11/25 · openalex publication_date 2006/11/29 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove upper bounds on angular momentum and centre of mass in terms of the Hamiltonian mass and cosmological constant for non-singular asymptotically anti-de Sitter initial data sets satisfying the dominant energy condition. We work in all space-dimensions larger than or equal to three, and allow a large class of asymptotic backgrounds, with spherical and non-spherical conformal infinities; in the latter case, a spin-structure compatibility condition is imposed. We give a large class of non-trivial examples saturating the inequality. We analyse exhaustively the borderline case in space-time dimension four: for spherical cross-sections of Scri, equality together with completeness occurs only in anti-de Sitter space-time. On the other hand, in the toroidal case, regular non-trivial initial data sets saturating the bound exist.