Summary
A static vacuum line-element is derived which represents the field of a collinear set of spherically symmetric masses. A limiting process applied to this line-element yields an explicit global solution of a problem first considered by Bondi: the field of two symmetrically placed mass-dipoles moving in radially opposite directions.
Riassunto
Si deduce un elemento statico di linea del vuoto che rappresenta il campo di un gruppo collineare di masse sfericamente simmetriche. Un processo di limite applicato a questo elemento di linea dà una soluzione globale esplicita di un problema già studiato da Bondi: il campo di due dipoli di massa, posti simmetricamente, che si muovono in direzioni radialmente opposte.
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References
P. Morrison:Am. Journ. Phys.,26, 358 (1958).
L. I. Schiff:Proc. Nat. Acad. Sci. U.S.A.,45, 69 (1959).
B. Hoffmann:Les Théories Relativistes de la Gravitation (Proceedings of the Royaumont conference), Centre National de la Recherche Scientifique (Paris, 1962), p. 237.
J. L. Synge:Relativity: The General Theory (Amsterdam, 1960), p. 314.
H. Bondi:Rev. Mod. Phys.,29, 423 (1957).
H. E. J. Curzon:Proc. Lond. Math. Soc.,23, xxix, 477 (1924). See alsoL. Silberstein:Phys. Rev.,49, 268 (1936);A. Einstein andN. Rosen:Phys. Rev.,49, 404 (1936).
E. Bach:Math. Zeits.,13, 134 (1922).
A. Palatini:Rend. Acc. Lincei,32, 263 (1923).
J. Chazy:Compt. Rend. Acad. Sci., Paris,177, 303, 939 (1923);Bull. Soc. Math., France,52, 17 (1924).
M. D. Kruskal:Phys. Rev.,119, 1743 (1960). See alsoR. W. Fuller andJ. A. Wheeler:Phys. Rev.,128, 919 (1962).
W. Rinow:Math Zeits.,35, 512 (1932).
G. Lemaître:Annales de la Societé Scientifique de Bruxelles, Ser. A,53, 82
H. P. Robertson:Lecture (Toronto, 1939), quoted byJ. L. Synge:Proc. Roy. Irish Acad.,53 A, 83 (1950). Synge’s own extension (given in this paper) is not a manifold.
D. Finkelstein:Phys. Rev.,110, 965 (1958).
C. Fronsdal:Phys. Rev.,116, 778 (1959).
J. L. Synge:Relativity: The General Theory, Chap. VIII (Amsterdam, 1960).
P. Jordan, J. Ehlers andW. Kundt:Akad. Wiss. Mainz, Abh. Math-Nat. Kl., Nr. 2, Kap. 3 (Jahrg., 1960).
E. T. Whittaker:Proc. Roy. Soc., A116, 720 (1927).
J. L. Stnge:Proc. Edinburgh Math. Soc.,11, 42 (1958).
W. B. Bonnor andN. S. Swaminarayan:Zetis. Phys.,177, 240 (1964).
K. A. Khan:Master’s Thesis, University of alberta (Edmonton, 1964).
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Israel, W., Khan, K.A. Collinear particles and bondi dipoles in general relativity. Nuovo Cim 33, 331–344 (1964). https://doi.org/10.1007/BF02750196
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DOI: https://doi.org/10.1007/BF02750196