11 research outputs found
Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
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.Comment: improvements in the presentation; some statements correcte