On the center of mass of asymptotically hyperbolic initial data sets

Cederbaum, Carla; Cortier, Julien; Sakovich, Anna

doi:10.1007/s00023-015-0438-5

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On the center of mass of asymptotically hyperbolic initial data sets

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Cortier, Julien
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Sakovich, Anna
Geometric Measure Theory, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Cederbaum, C., Cortier, J., & Sakovich, A. (2015). On the center of mass of asymptotically hyperbolic initial data sets. Annales Henri Poincaré, 1-24. doi:10.1007/s00023-015-0438-5.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0024-A657-8

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.