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Journal Article

Rigid upper bounds for the angular momentum and centre of mass


Chrusciel,  Piotr T.
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Chrusciel, P. T., Maerten, D., & Tod, P. (2006). Rigid upper bounds for the angular momentum and centre of mass. Journal of High Energy Physics, 2006(11): 084.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-4C41-A
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.