Abstract
The asymptotic symmetries and the conserved quantities of asymp- totically flat spacetimes are investigated by extending the canonical analysis of vacuum general relativity of Beig and ´ O Murchadha. It is shown that the algebra of asymptotic Killing symmetries, defined with respect to a given foliation of the spacetime, depends on the fall-off rate of the metric. It is only the Lorentz Lie algebra for slow fall-off, but it is the Poincarea lgebra for 1 /r or faster fall-off. The energy-momentum and (relativistic) angular momentum are defined by the value of the Beig- ´ O Murchadha Hamiltonian with lapse and shift corresponding to asymptotic Killing vectors. While this energy-momentum and spatial angular momentum reproduce the familiar ADM energy-momentum and Regge-Teitelboim angular momentum, respectively, the centre-of-mass deviates from that of Beig and ´ O Murchadha. The new centre-of-mass is conserved, and, together with the spatial angular momentum, form an anti-symmetric Lorentz tensor which transforms just in the correct way under asymptotic Poincare transformations of the asymptotically Cartesian coordinate system.
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