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Cited by 175Relativity and Gravitational TheoryBlack Holes and Theoretical PhysicsCosmology and Gravitation Theories

Spatial infinity as a boundary of spacetime

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Ashtekar, A, Romano, J D·1992·Classical and Quantum Gravity
DOI 10.1088/0264-9381/9/4/019
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Abstract

A definition of asymptotic flatness at spatial infinity is given by imposing conditions at a time-like boundary of a completed 4-manifold. The resulting framework is similar to the Penrose description of asymptotic flatness at null infinity in that physics at spatial infinity is coded in smooth tensor fields on the boundary. it reproduces the standard results of the i 0 -framework with the advantage that it avoids the awkward differentiability conditions imposed at i 0 . The universal structure made available by the definition is examined and the structure of the associated asymptotic symmetry group is analysed. The tensor fields describing the leading order behaviour of the gravitational field at spatial infinity are then introduced and the field equations that they satisfy are derived. Finally, the expressions of the 4-momentum and the angular momentum are presented. The structure of the permissible isometry groups in asymptotically flat spacetimes is discussed in an appendix.

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  • There are other relevant topologies in state space, as the norm topologies defined by the kinematical or diffeomorphism-invariant Hilbert structures, which are inequivalent to the one in which the limit (13) is taken.

    “note for instance that there are other relevant topologies in state space, as the norm topologies defined by the kinematical or diffeomorphism-invariant Hilbert structures [6, 7], which are inequivalent to the one in which the limit (13) is taken.”

    From Discreteness of area and volume in quantum gravity (1995) · cites this paper as [7]

    The passages in §4, “Asymptotic symmetries” (page not supplied), discuss equivalence of spacetime completions, not topologies on a state space. Searches for Hilbert norm topologies and inequivalent state-space limits found no passage addressing the attributed claim. (LLM, conf=0.76)

    Experimental — accuracy not yet measured

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Research works printed but not linked: 1

  1. Amwit1 R, Deser S and Misner C W 1960 Phys. Reu 117 1695; 1960 Phy. Rev. 118 lIW, 1961 %s Rm 121 IMh; 1961 Phys. Reu U 2 997; I962 Gmvirarinn, mi Ifmodurhn IO Cwm Resew& ed L Witen (New York Wiley)

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Authors
Ashtekar, A., & Romano, J. D.
Affiliations
Syracuse University (US)
ORCID
Venue
Classical and Quantum Gravity
Publisher
IOP Publishing
Published
1992-04-01
Volume
9
Issue
4
Pages
1069-1100
ISSN
  • 0264-9381 (ISSN-L)
  • 1361-6382
DOI
10.1088/0264-9381/9/4/019
OpenAlex
W2051985377
Cited by
175
References
28
Citations by year
2026: 4 · 2025: 8 · 2024: 8 · 2023: 1 · 2022: 9 · 2021: 4 · 2020: 4 · 2019: 23 · 2018: 10 · 2017: 4 · 2016: 2 · 2015: 3 · 2014: 3 · 2013: 5 · 2012: 6
FWCI
7.90
Type
journal article
Language
en
Open access
Locations
Classical and Quantum Gravity (publishedVersion)
Topics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Relativity and Gravitational Theory
  • Physical Sciences › Physics and Astronomy › Nuclear and High Energy Physics › Black Holes and Theoretical Physics
  • Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
Keywords
asymptotically flat spacetimes, spatial infinity, asymptotic symmetry group, angular momentum, isometry groups

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