Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times

Journal article

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.

Authors: Chrusciel, P; Maerten, D; Tod, P

• Journal: JHEP
• Volume: 0611
• Issue: 11
• Pages: 084
• Publication date: 2006-06-14
• DOI: 10.1088/1126-6708/2006/11/084
• EISSN: 1029-8479
• ISSN: 1029-8479
• Language: English
• Keywords: hep-th; gr-qc