On the Center of Mass of Asymptotically Hyperbolic Initial Data Sets

2015/01/22 by Carla Cederbaum, Julien Cortier, Anna Sakovich · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Center (category theory) #Center of mass (relativistic) #Cosmology and Gravitation Theories #Einstein #Euclidean geometry #Hamiltonian (control theory) #Noncommutative and Quantum Gravity Theories #Stability theory #gr-qc #math.AP #math.DG

paper · pdf · doi:10.1007/s00023-015-0438-5

arxiv created 2015/01/22 · openalex publication_date 2015/10/20 · arxiv updated 2016/05/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We define the (total) center of mass for suitably asymptotically hyperbolic time-slices of asymptotically anti-de Sitter spacetimes in general relativity. We do so in analogy to the picture that has been consolidated for the (total) center of mass of suitably asymptotically Euclidean time-slices of asymptotically Minkowskian spacetimes (isolated systems). In particular, we unite -- an altered version of -- the approach based on Hamiltonian charges with an approach based on CMC-foliations near infinity. The newly defined center of mass transforms appropriately under changes of the asymptotic coordinates and evolves in the direction of an appropriately defined linear momentum under the Einstein evolution equations.

Citations

• Rigid upper bounds for the angular momentum and centre of mass of non-singular asymptotically anti-de Sitter space-times
• The mass of an asymptotically flat manifold
• Definition of center of mass for isolated physical systems and unique foliations by stable spheres with constant mean curvature

Cited by

• The mass in terms of Einstein and Newton