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Quasilocal Center-of-Mass for Teleparallel Gravity

Asymptotically flat gravitating systems have 10 conserved quantities, which lack proper local densities. It has been hoped that the teleparallel equivalent of Einstein's GR (TEGR, aka GR${}_{||}$) could solve this gravitational energy-momentum localization problem. Meanwhile a new idea: quasilocal quantities, has come into favor. The earlier quasilocal investigations focused on energy-momentum. Recently we considered quasilocal angular momentum for the teleparallel theory and found that the popular expression (unlike our ``covariant-symplectic'' one) gives the correct result only in a certain frame. We now report that the center-of-mass moment, which has largely been neglected, gives an even stronger requirement. We found (independent of the frame gauge) that our ``covariant symplectic'' Hamiltonian-boundary-term quasilocal expression succeeds for all the quasilocal quantities, while the usual expression cannot give the desired center-of-mass moment. We also conclude, contrary to hopes, that the teleparallel formulation appears to have no advantage over GR with regard to localization.