Abstract:
The Poisson brackets of the generators of the Hamiltonian formalism for general
relativity are obtained with allowance for surface terms of arbitrary form. For
Minkowski space there exists the asymptotic Poincaré group, which is the semidirect
product of the Poincaré group and an infinite subgroup for which the algebra
of generators with surface terms closes. A criterion invariant with respect to
the choice of the coordinate system on the hypersurfaces is obtained for realization
of the Poincaré group in asymptotically flat space-time. The “background” fiat
metric on the hypersurfaces and Poincaré group that preserve it are determined
nonuniquely; however, the numerical values of the generators do not depend on the
freedom of this choice on solutions of the constraint equations. For an asymptotically
Galilean metric, the widely used boundary conditions are determined more accurately.
A prescription is given for application of the Arnowitt–Deser–Misner decomposition
in the case of a slowly decreasing contribution from coordinate and time transformations.
Citation:
V. O. Soloviev, “Generator algebra of the asymptotic Poincaré group in the general theory of relativity”, TMF, 65:3 (1985), 400–414; Theoret. and Math. Phys., 65:3 (1985), 1240–1249
\Bibitem{Sol85}
\by V.~O.~Soloviev
\paper Generator algebra of the asymptotic Poincar\'e group in the general theory of relativity
\jour TMF
\yr 1985
\vol 65
\issue 3
\pages 400--414
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\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 65
\issue 3
\pages 1240--1249
\crossref{https://doi.org/10.1007/BF01036133}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1985D277400008}
Linking options:
https://www.mathnet.ru/eng/tmf5147
https://www.mathnet.ru/eng/tmf/v65/i3/p400
This publication is cited in the following 11 articles:
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A. E. Pavlov, “Intrinsic time in Wheeler–DeWitt conformal superspace”, Gravit. Cosmol., 23:3 (2017), 208
Lompay R.R. Petrov A.N., “Covariant Differential Identities and Conservation Laws in Metric-Torsion Theories of Gravitation. I. General Consideration”, J. Math. Phys., 54:6 (2013), 062504
Pitts, JB, “Null cones and Einstein's equations in Minkowski spacetime”, Foundations of Physics, 34:2 (2004), 211
L szl B Szabados, “On the roots of the Poincar structure of asymptotically flat spacetimes”, Class. Quantum Grav., 20:13 (2003), 2627
Roberto De Pietri, Luca Lusanna, Luca Martucci, Stefano Russo, “Review: Dirac's Observables for the Rest-Frame Instant Form of Tetrad Gravity in a Completely Fixed 3-Orthogonal Gauge”, General Relativity and Gravitation, 34:6 (2002), 877
Luca Lusanna, “REVIEW: The Rest-Frame Instant Form of Metric Gravity”, General Relativity and Gravitation, 33:9 (2001), 1579
Soloviev, VO, “Black hole entropy from Poisson brackets: Demystification of some calculations”, Physical Review D, 6102:2 (2000), 027502
Soloviev V.O., “Black hole entropy from Poisson brackets: Demystification of some calculations”, Physical Review D, 61:2 (2000), 027502
V. O. Soloviev, “Poisson algebra independent on boundary conditions in Ashtekar's formalism”, Theoret. and Math. Phys., 112:1 (1997), 906–921
A Dimakis, F Muller-Hoissen, “Spinor fields and the positive energy theorem”, Class. Quantum Grav., 7:3 (1990), 283
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