The Poincaré Structure and the Centre-of-Mass of Asymptotically Flat Spacetimes

  • László B. Szabados
Part of the Lecture Notes in Physics book series (LNP, volume 692)


The asymptotic symmetries and the conserved quantities of asymptotically flat spacetimes are investigated by extending the canonical analysis of vacuum general relativity of Beig and Ó 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 Poincaré algebra for 1/r or faster fall-off. value of the Beig–Ó 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 Ó 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 Poincaré transformations of the asymptotically Cartesian coordinate system.


Angular Momentum Minkowski Spacetime Asymptotic Symmetry Spacelike Hypersurface Poisson Algebra 
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© Springer 2006

Authors and Affiliations

  • László B. Szabados
    • 1
  1. 1.Research Institute for Particle and Nuclear PhysicsHungarian Academy of SciencesHungary

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