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.
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Communicated by James A. Isenberg.
The authors are grateful to the MSRI, Berkeley, to the FIM, ETH Zürich, to the AEI, Potsdam, and to the MPIM Bonn for hospitality and financial support during part of this work. Carla Cederbaum is indebted to the Baden-Württemberg Stiftung for the financial support of this research project by the Eliteprogramme for Postdocs. Julien Cortier benefits from an EPDI fellowship during his stay at ETH and MPIM. This paper is typeset in \({\hbox{\LaTeX}}\) with extra packages by Chr. Nerz.
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Cederbaum, C., Cortier, J. & Sakovich, A. On the Center of Mass of Asymptotically Hyperbolic Initial Data Sets. Ann. Henri Poincaré 17, 1505–1528 (2016). https://doi.org/10.1007/s00023-015-0438-5
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DOI: https://doi.org/10.1007/s00023-015-0438-5