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Quasilocal Center-of-Mass

James M. Nester·Feng-Feng Meng·Chiang-Mei Chen
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Abstract

Gravitating systems have no well-defined local energy-momentum density. Various quasilocal proposals have been made, however the center-of-mass moment (COM) has generally been overlooked. Asymptotically flat graviating systems have 10 total conserved quantities associated with the Poincar{é} symmetry at infinity. In addition to energy-momentum and angular momentum (associated with translations and rotations) there is the boost quantity: the COM. A complete quasilocal formulation should include this quantity. Getting good values for the COM is a fairly strict requirement, imposing the most restrictive fall off conditions on the variables. We take a covariant Hamiltonian approach, associating Hamiltonian boundary terms with quasilocal quantities and boundary conditions. Unlike several others, our {\it covariant symplectic} quasilocal expressions do have the proper asymptotic form for all 10 quantities.

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James M. Nester, Feng-Feng Meng, Chiang-Mei Chen. 2004-04-27. Quasilocal Center-of-Mass. https://arxiv.org/abs/gr-qc/0403103

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