Nester-Chen 準局域表示式在 Teleparallel 理論及廣義相對論中，可以使能量、動量、角動量及質心距的準局域化 (quasilocalization) 成為協變的 (covariant) ，而此篇論文要討論的是：Teleparallel理論中的準局域質心距，在Nester-Chen 準局域表示式裡佔有重要地位。 Asymptotically flat gravitating system have 10 conserved quantities associated with Poincar´e symmetry, which lack proper local densities. It has been hoped that the tetrad formulation and the related teleparallel equivalent of Einstein’s GR (TEGR, aka GR{II}) could solve this longstanding gravitational energy-momentum localization problem [23, 32, 33]. Quasilocal expressions are now favored. Earlier quasilocal GR{II} investigations focused on energy-momentum [32, 33]. Recently our group considered angular momentum and found that the popular expression (unlike our “covariantsymplectic” one [5]) was not asymptotically locally Lorentz frame gauge invariant; it gives the correct result but only in a certain frame [30]. The remaining Poincar´e quantity, the center-of-mass moment, has been neglected. Obtaining the correct value for this quantity is a quite severe requirement, hence a new discriminating test for proposed expressions. We found (independent of the frame gauge choice) that the GR{II} “covariant-symplectic” Hamiltonian-boundary-term quasilocal expression succeeds while the usual expression does not give the desired center-of-mass moment. None of the tetrad expressions gives the desired center-of-mass moment. We conclude that the teleparallel formulation is definitely better than the tetrad formulation, and the covariant-symplectic expressions are definitely better than the alternatives. We also found however that GR{II} has no advantage over GR for energy localization.
