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

Abstract

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.

improvements in the presentation; some statements corrected

References in corpus (3)

• The Trautman-Bondi mass of initial data sets
• Non-trivial, static, geodesically complete space-times with a negative cosmological constant II. $n\ge 5$
• Positive energy-momentum theorem in asymptotically anti de Sitter space-times

Cited by in corpus (13)

• Instability of Rotating Anti-de Sitter Black Holes
• Metrics of Eguchi-Hanson types with the negative constant scalar curvature
• On the black hole species (by means of natural selection)
• Spacetime Harmonic Functions and Applications to Mass
• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• Optimal eigenvalue estimate for the Dirac-Witten operator on bounded domains with smooth boundary
• On Mason's rigidity theorem
• Penrose's quasi-local mass for asymptotically anti-de Sitter space-times
• Evidence for NO violation of the second law in extended black hole thermodynamics
• Existence and uniqueness of constant mean curvature foliations of general asymptotically hyperbolic 3-manifolds
• Positivity of holographic energy
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS
• Hyperbolic positive energy theorem with electromagnetic fields