The DOI matches its Crossref record; 28 of the 28 references it cites were found in a registry or an index.
Spatial infinity as a boundary of spacetime
Open accessAbstract
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
The check wasn’t confident either way, so it gives no verdict — never disputed.
In the citing paper
“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]
Experimental — accuracy not yet measured
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
Bondi, H., Van der Burg, M. G. J., & Metzner, A. W. K. (1962) · Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences · doi:10.1098/rspa.1962.0161 · Cited by 2,426
Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
Sachs, R. K. :. (1962) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1962.0206 · Cited by 1,860
Black holes in general relativity
Hawking, S. W. (1972) · Communications in Mathematical Physics · doi:10.1007/bf01877517 · Cited by 1,561
Asymptotic Symmetries in Gravitational Theory
Sachs, R. K. (1962) · Physical Review · doi:10.1103/physrev.128.2851 · Cited by 993
Empty-Space Generalization of the Schwarzschild Metric
Newman, E. T., Tamburino, L. A., & Unti, T. W. J. (1963) · Journal of Mathematical Physics · doi:10.1063/1.1704018 · Cited by 857
Zero rest-mass fields including gravitation: asymptotic behaviour
Penrose, R. (1965) · Proceedings of the Royal Society of London A Mathematical and Physical Sciences · doi:10.1098/rspa.1965.0058 · Cited by 853
Asymptotic Properties of Fields and Space-Times
Penrose, R. (1963) · Physical Review Letters · doi:10.1103/physrevlett.10.66 · Cited by 785
Coordinate Invariance and Energy Expressions in General Relativity
Arnowitt, R., Deser, S., & Misner, C. W. (1961) · Physical Review · doi:10.1103/physrev.122.997 · Cited by 576
The Flatter Regions of Newman, Unti, and Tamburino's Generalized Schwarzschild Space
Misner, C. W. (1963) · Journal of Mathematical Physics · doi:10.1063/1.1704019 · Cited by 573
Ashtekar, A., & Hansen, R. O. (1978) · Journal of Mathematical Physics · doi:10.1063/1.523863 · Cited by 480
Self-citation
Research works printed but not linked: 1
- Arnowitt R, 1960, 117, 1695
Cited by
Sorted by citations
Items 101–175 of 175
Calculating asymptotic quantities near space‐like and null infinity from Cauchy data
Friedrich, H., & Kánnár, J. (2000) · Annalen der Physik · doi:10.1002/andp.200051203-514 · Cited by 11
On the Various Extensions of the BMS Group
Ruzziconi, R. (2020) · Dépôt institutionnel de l'Université libre de Bruxelles (Université Libre de Bruxelles) · doi:10.48550/arxiv.2009.01926 · Cited by 11
BMS-supertranslation charges at the critical sets of null infinity
Mohamed, M. M. A., Prabhu, K., & Kroon, J. A. V. (2024) · Journal of Mathematical Physics · doi:10.1063/5.0187927 · Cited by 10
Timelike infinity and asymptotic symmetry
Gen, U., & Shiromizu, T. (1998) · Journal of Mathematical Physics · doi:10.1063/1.532666 · Cited by 10
Superrotations at spacelike infinity
Fiorucci, A., Matulich, J., & Ruzziconi, R. (2024) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.110.l061502 · Cited by 10
Supertranslations and holographic stress tensor
Amitabh Virmani, C. (2012) · Journal of High Energy Physics · doi:10.1007/jhep02(2012)024 · Cited by 10
Energy in higher-dimensional spacetimes
Barzegar, H., Chruściel, P. T., & Hörzinger, M. (2017) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.96.124002 · Cited by 10
Spatial infinity in higher dimensional spacetimes
Shiromizu, T., & Tomizawa, S. (2004) · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · doi:10.1103/physrevd.69.104012 · Cited by 10
The Ashtekar-Hansen universal structure at spatial infinity is weakly pseudo-CarrollianPreprint
Gibbons, G. W. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1902.09170 · Cited by 10
Tetrad Gravity and Dirac's ObservablesPreprint
Lusanna, L. (2000) · Cited by 10
Supertranslations at timelike infinity
Chakraborty, S., Ghosh, D., Hoque, S. J., Khairnar, A., & Amitabh Virmani, C. (2022) · Journal of High Energy Physics · doi:10.1007/jhep02(2022)022 · Cited by 9
Strings as perturbations of evolving spin networks
Smolin, L. (2000) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(00)00758-1 · Cited by 25
Bondi-Metzner-Sachs invariance and electric-magnetic duality
Bunster, C., Gomberoff, A., & Pérez, A. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.101.044003 · Cited by 8
Source and response soft charges for Maxwell theory on AdSd
Esmaeili, E., Hosseinzadeh, V., & Sheikh-Jabbari, M. M. (2019) · Journal of High Energy Physics · doi:10.1007/jhep12(2019)071 · Cited by 8
Bruegmann, B. (1993) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9303015 · Cited by 8
Schilling, T. A. (1994) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9409031 · Cited by 7
Carrollian partition function for bulk Yang-Mills theory
Kraus, P., & Myers, R. M. (2025) · Journal of High Energy Physics · doi:10.1007/jhep08(2025)180 · Cited by 6
Holographic renormalization of asymptotically flat gravity
Park, M., & Mann, R. B. (2012) · Journal of High Energy Physics · doi:10.1007/jhep12(2012)098 · Cited by 6
Quantum gravity and the algebra of tangles
Baez, J. C. (1993) · Classical and Quantum Gravity · doi:10.1088/0264-9381/10/4/006 · Cited by 9
Beetle, C., & Corichi, A. (1997) · arXiv (Cornell University) · doi:10.48550/arxiv.gr-qc/9703044 · Cited by 6
On conserved quantities at spatial infinity
Perng, S.-M. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532841 · Cited by 5
Spacetimes which are asymptotic to certain Friedman-Robertson-Walker spacetimes at timelike infinity
Shiromizu, T., & Gen, U. (1999) · Classical and Quantum Gravity · doi:10.1088/0264-9381/16/9/313 · Cited by 5
Towards a background independent approach to M theory
Smolin, L. (1999) · Chaos Solitons & Fractals · doi:10.1016/s0960-0779(98)00206-9 · Cited by 15
Deformation of Asymptotic Symmetry Algebras and Their Physical RealizationsPreprint
Safari, H. R. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2011.02318 · Cited by 5
Log translation invariance of log soft gravitational radiation
Boschetti, G., & Campiglia, M. (2025) · Journal of High Energy Physics · doi:10.1007/jhep10(2025)105 · Cited by 4
Asymptotic symmetries of projectively compact order one Einstein manifolds
Borthwick, J., & Herfray, Y. (2024) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2023.0042 · Cited by 4
Non-Inertial Frames and Dirac Observables in Relativity
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239 · Cited by 4
Electric and magnetic aspects of gravitational theoriesPreprint
Dehouck, F. (2011) · arXiv (Cornell University) · doi:10.48550/arxiv.1112.3962 · Cited by 4
Holographic Renormalization of Asymptotically Flat GravityPreprint
Park, M., & Mann, R. B. (2016) · Cited by 4
Ti and Spi, Carrollian extended boundaries at timelike and spatial infinity
Borthwick, J., Chantreau, M., & Herfray, Y. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/ae0d3f · Cited by 3
Compère, G., & Robert, S. (2026) · Journal of Mathematical Physics · doi:10.1063/5.0318928 · Cited by 3
Balachandran, A. P., & Reyes-Lega, A. F. (2019) · Springer proceedings in physics · doi:10.1007/978-3-030-24748-5_4 · Cited by 3
Calculation of asymptotic charges at the critical sets of null infinity
Mohamed, M. M. A. (2024) · Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rsta.2023.0038 · Cited by 3
Asymptotically Schwarzschild space–times
Gen, U., & Shiromizu, T. (1999) · Journal of Mathematical Physics · doi:10.1063/1.532848 · Cited by 3
Embedded graph invariants in Chern-Simons theory
Major, S. A. (1999) · Nuclear Physics B · doi:10.1016/s0550-3213(99)00164-9 · Cited by 3
Hamiltonian structure and constraint algebra in the (2+2) formalism
Yoon, J. H. (2014) · Classical and Quantum Gravity · doi:10.1088/0264-9381/31/4/045005 · Cited by 3
Timelike Infinity and Asymptotic Symmetry
Gen, U., & Shiromizu, T. (1997) · CERN Document Server (European Organization for Nuclear Research) · Cited by 3
Quasi-local energy-momentum and the Sen geometry of two-surfaces
Szabados, L. (1997) · Banach Center Publications · doi:10.4064/-41-1-205-219 · Cited by 3
Embedded graph invariants in Chern-Simons theoryPreprint
Major, S., & Wien, U. (1998) · Cited by 3
The Generalised Conformal Field Equations Near Spatial Infinity
Doulis, G. (2013) · Otago University Research Archive (University of Otago) · Cited by 3
From spatial to null infinity: Connecting initial data to peeling
Schneider, B., & Khera, N. (2025) · Physical review. D/Physical review. D. · doi:10.1103/hcx1-hcf9 · Cited by 2
BMS Representations for Generic Supermomentum
Xavier Bekaert, A., & Herfray, Y. (2026) · Communications in Mathematical Physics · doi:10.1007/s00220-025-05513-0 · Cited by 2
A holographic entanglement entropy at spi
Ghosh, A., & Krishnan, C. (2024) · Journal of High Energy Physics · doi:10.1007/jhep06(2024)068 · Cited by 2
Borthwick, J., & Herfray, Y. (2024) · Geometriae Dedicata · doi:10.1007/s10711-024-00973-5 · Cited by 2
Tetrad gravity and Dirac's observables
Lusanna, L. (2000) · Nuclear Physics B - Proceedings Supplements · doi:10.1016/s0920-5632(00)00790-8 · Cited by 2
Asymptotic flatness in higher dimensions
Cameron, P., & Chruściel, P. T. (2022) · Journal of Mathematical Physics · doi:10.1063/5.0083728 · Cited by 2
On the total energy conservation of the Alcubierre spacetime
Carneiro, F. L., Ulhoa, S. C., Maluf, J. W., & da Rocha-Neto, J. F. (2022) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/07/030 · Cited by 2
Supertranslations at spatial and timelike infinities in the first-order formalism
Solanki, D. N., & Bhattacharjee, S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.111.024033 · Cited by 1
On the singularities of the exponential function of a semidirect product
Chirvăsitu, A., Dahmen, R., Neeb, K., & Schmeding, A. (2025) · Classical and Quantum Gravity · doi:10.1088/1361-6382/add786 · Cited by 1
Null infinity as a Killing horizon
Alves, N. D. A., & Landulfo, A. G. S. (2025) · Physical review. D/Physical review. D. · doi:10.1103/tf22-2r6y · Cited by 1
An asymptotic proof of the classical log soft graviton theorem
Boschetti, G., & Campiglia, M. (2026) · Journal of High Energy Physics · doi:10.1007/jhep06(2026)222 · Cited by 1
Melas, E. (2011) · Journal of Physics Conference Series · doi:10.1088/1742-6596/283/1/012023 · Cited by 1
Quasi-local instantaneous charges asymptotics at spatial infinity
Jezierski, J., & Smołka, T. (2022) · General Relativity and Gravitation · doi:10.1007/s10714-022-02912-9 · Cited by 1
BMS symmetries of gravitational scattering
Kervyn, X. (2025) · Nuclear Physics B · doi:10.1016/j.nuclphysb.2025.116948 · Cited by 1
Black Holes: New Perspectives from Higher Dimensions
Haddad, N. (2012) · LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Científicas)
Espaços-tempos assintoticamente planos
Annibale, E. S. (2007) · doi:10.11606/d.45.2007.tde-06052007-191653
Relativistic Perfect Fluids and Covariant Thermodynamics
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.014
Galilei and Minkowski Space-Times
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.002
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.001
ADM Tetrad Gravity and Its Constraints
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.007
Grassmann Variables and Pseudo–Classical Lagrangians
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.013
Singular Lagrangians and Constraint Theory
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.009
Relativistic Dynamics and the Relativistic Center of Mass
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.004
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.010
Post-Minkowskian and Post-Newtonian Approximations
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.008
Matter in the Rest-Frame Instant Form of Dynamics
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.005
Concluding Remarks and Open Problems
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.011
Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.012
Hamiltonian Gravity in Einstein Space-Times
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.006
Global Non-Inertial Frames in Special Relativity
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.003
Lusanna, L. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108691239.015
Report on scipost_202205_00018v1
(2022) · SciPost Physics · doi:10.21468/scipost.report.5261
Report on scipost_202205_00018v1
(2022) · SciPost Physics · doi:10.21468/scipost.report.5212
Report on scipost_202205_00018v1
(2022) · SciPost Physics · doi:10.21468/scipost.report.5194
Interacting fields at spatial infinity
Anupam, A. H., Athira, P. V., Paul, P., & Raju, S. (2026) · Physical review. D/Physical review. D. · doi:10.1103/hm1z-qbfw
Metadata
- Authors
- Ashtekar, A., & Romano, J. D.
- Affiliations
- Syracuse University (US)
- 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
- 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
- bronze
- doi.org
- 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
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
