Abstract
An asymptotic symmetries theorem is proved under certain hypotheses on the behaviour of the metric at spatial infinity. This implies that the Einstein-von Freud-ADM mass can be invariantly assigned to an asymptotically flat four dimensional end of an asymptotically empty solution of Einstein equations if the metric is a no-radiation metric or if the end is defined in terms of a collection of boost-type domains.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abbott, L. F., Deser, S.: Stability of gravity with a cosmological constant. Nucl. Phys.B195, 76–96 (1982)
Arnowitt, R., Deser, S., Misner, C. W.: The dynamics of general relativity. In: Gravitation, on introduction to current research. Witten L. (ed). New York: J. Wiley 1962
Ashtekar, A.: Asymptotic structure of the gravitational field. In: General relativity and gravitation: one hundred years after the birth of albert Einstein. vol. 2, Held A. (ed.), pp. 37–70. New York: Plenum Press 1980
Ashtekar, A., Hansen, R. O.: A unified treatment of null and spatial infinity in general relativity. I. Universal structure, asymptotic symmetries and conserved quantities at spatial infinity. J. Math. Phys.19, 1542–1566 (1978)
Bartnik, R.: The mass of an asymptotically flat manifold. Commun. Pure Appl. Math.39, 661–693 (1986)
Bizoń, P. Malec, E.: On Witten's positive energy proof for weakly asymptotically flat space-times. Class. Quantum Grav.3, L123-L128 (1986)
Chruściel, P. T.: Boundary conditions at spatial infinity from a Hamiltonian point of view. In: Topological properties and global structure of space-time. Bergmann P. G., Sabbata, V.de (eds.), pp. 49–59. New York: Plenum Press 1986
Chruściel, P. T.: A remark on the positive energy theorem. Class. Quantum Grav.3, L115-L121 (1986)
Chruściel, P. T., Kondracki, W.: Some global charges in classical yang-mills theory. Phys. Rev.D36, 1874–1881 (1987)
Christodoulou, D. O'Murchadha, N.: The boost problem in general relativity. Commun. Math. Phys.80, 271–300 (1981)
Einstein, A.: Die Grundlage der allgemeinen Relativitaets-Theorie. Ann. Phys.49, 769–822 (1916)
Freud, Ph.v: Ueber die Ausdruecke der Gesamtenergie und des Gesamtimpulses eines materiellen Systems in der allgemeinen Relativitaets-Theorie. Ann. Math.40, 417–419 (1939)
Geroch, R.: Structure of the Gravitational Field at Spatial Infinity. J. Math. Phys.13, 956–968 (1972)
O'Murchadha, N.: Total energy-momentum in general relativity. J. Math. Phys.27, 2111–2128 (1986)
Solovyev, V. O.: Generator algebra of the asymptotic Poincaré group in the general theory of relativity. Theor. Math. Phys.65, 400–414 (1985)
Sommers, P.: The geometry of the gravitational field at spatial infinity. J. Math. Phys.19, 549–554 (1978)
Trautman, A.: Conservation laws in general relativity, the same book as [ADM]
Weinberg, S.: Gravitation and cosmology. New York: J. Wiley 1972
Author information
Authors and Affiliations
Additional information
Communicated by S.-T. Yau
On leave of absence from the Institute of Mathematics, Polish Academy of Sciences, Warsaw, Poland
Supported in part by the Polish Ministry of Science Research Project CPBP 01.2 and by the NSF Grant PHY8503072 to Yale University
Rights and permissions
About this article
Cite this article
Chruściel, P.T. On the invariant mass conjecture in general relativity. Commun.Math. Phys. 120, 233–248 (1988). https://doi.org/10.1007/BF01217963
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01217963