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On the center of mass of asymptotically hyperbolic initial data sets

MPG-Autoren
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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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1501.05559.pdf
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Zitation

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.


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