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Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves

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Abstract

A class of the asymptotically Euclidian space-times is shown to exist for which the Schwarzschild mass is equal to zero. The coordinate atlases of these space-times satisfy two additional conditions: δ k (-gg 0k)=0 and σ 0ik δ ik0g - σ k ik δ 0i0g =0. In aT-orthogonal metricgs 2=g 00 dt 2 -g αβ dx α dx β these conditions take a simple form: δ0(detg αβ)=0 and (δ0 g αβ)(δ0 g αβ)=0.

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References

  • Araki, H. (1959).Annals of Physics,7, 456.

    Google Scholar 

  • Arnowitt, S., Deser, S. and Misner, C. (1960).Annals of Physics,11, 116.

    Google Scholar 

  • Bauer, H. (1918).Physikalische Zeitschrift,19, 163.

    Google Scholar 

  • Bergmann, P. G. and Brunnings, J. H. M. (1948).Review of Modern Physics,21, 480.

    Google Scholar 

  • Bergmann, P. G. (1949).Physical Review,75, 680.

    Google Scholar 

  • Bergmann, P. G., Penfield, R., Schiller, R. and Zatzkis, H. (1950).Physical Review,80, 81.

    Google Scholar 

  • Bergmann, P. G. and Thomson, R. (1953).Physical Review,89, 400.

    Google Scholar 

  • Bergmann, P. G. (1956). InJubliee of Relativity Theory. Birkhauser Verlag, Basel.

    Google Scholar 

  • Bessel-Hagen, E. (1921).Annals of Mathematics,84, 258.

    Google Scholar 

  • Bondi, H. (1957).Nature (London),179, 1072.

    Google Scholar 

  • Bondi, H., Pirani, F. and Robinson, I. (1959).Proceedings of the Royal Society,A251, 519.

    Google Scholar 

  • Bondi, H., Van der Burg, M. and Metzner, A. (1962).Proceedings of the Royal Society,269, 21.

    Google Scholar 

  • Bonnor, W. B. (1959).Philosophical Transactions of the Royal Society,A251, 233.

    Google Scholar 

  • Bonnor, W. B. and Rotenberg, M. A. (1961).Proceedings of the Royal Society,A265, 109.

    Google Scholar 

  • Bonnor, W. B. and Rotenberg, M. A. (1966).Proceedings of the Royal Society,289, 247.

    Google Scholar 

  • Born, M. (1937).Annales de l'Institut Henri Poincaré,7, 155.

    Google Scholar 

  • Brdicka, M. (1951).Proceedings of the Royal Irish Academy,A54, 137.

    Google Scholar 

  • Brill, D. R. (1959).Annals of Physics,7, 466.

    Google Scholar 

  • Brill, D. R., Deser, S. and Faddeev, L. D. (1968).Physics Letters,A-26, 538.

    Google Scholar 

  • Brill, D. R. and Deser, S. (1968).Physical Review Letters,20, 75.

    Google Scholar 

  • Cahen, M. and Sengier-Diels, J. (1963).Bulletin de l'Académie r. de Belgique, Classe des Sciences,49, 43.

    Google Scholar 

  • Capella, M. A. (1961).Comptes Rendus Hebdomadaire des Séances de l'Académie des Sciences, Paris,252, 3940.

    Google Scholar 

  • De Donder, T. (1921).La Gravifique Einsteinienne. Paris.

  • De Wet, J. S. (1947).Proceedings of the Cambridge Philosophical Society,43, 511.

    Google Scholar 

  • Eddington, A. S. (1923).The Mathematical Theory of Relativity. University Press, Cambridge.

    Google Scholar 

  • Einstein, A. (1916).Sitzungsberichte der Preussischen Akademie der Wissenschaften,2, 1111.

    Google Scholar 

  • Fok, V. A. (1961).Theory of Space, Time and Gravitation. Publishing House of Phys.-Math. Literature, Moscow.

    Google Scholar 

  • Folomeshkin, V. N. (1967).Yadernaya Fizika,6, 1080.

    Google Scholar 

  • Folomeshkin, V. N. (1969).Acta Physica Polonica,36, 439.

    Google Scholar 

  • Folomeshkin, V. N. (1970).Acta Physica Polonica,B1, 13.

    Google Scholar 

  • Folomeshkin, V. N. (1971). Institute of High Energy Physics Preprint, IHEP 71–120, Serpukhov.

  • Folomeshkin, V. N. (1972). Institute of High Energy Physics Preprint, IHEP 72–92, Serpukhov.

  • Folomeshkin, V. N. (1974).International Journal of Theoretical Physics, Vol. 10, No. 3, p. 145.

    Google Scholar 

  • Fletcher, J. (1960).Review of Modern Physics,32, 65.

    Google Scholar 

  • Goldberg, J. N. (1953).Physical Review,89, 263.

    Google Scholar 

  • Goldberg, J. N. (1958).Physical Review,111, 315.

    Google Scholar 

  • Havas, P. and Goldberg, J. N. (1962).Physical Review,128, 398.

    Google Scholar 

  • Hilbert, D. (1915).Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse,3, 395.

    Google Scholar 

  • Hilbert, D. (1924).Annals of Mathematics,92, 1.

    Google Scholar 

  • Hill, E. L. (1951).Review of Modern Physics,23, 253.

    Google Scholar 

  • Hu, N. (1947).Proceedings of the Royal Irish Academy,A51, 87.

    Google Scholar 

  • Infeld, L. and Sheidegger, A. E. (1951).Canadian Journal of Mathematics,3, 195.

    Google Scholar 

  • Infeld, L. (1953).Canadian Journal of Mathematics,5, 17.

    Google Scholar 

  • Infeld, L. (1956).Annals of Mathematics,17, 545.

    Google Scholar 

  • Infeld, L. (1959).Annals of Physics,16, 341.

    Google Scholar 

  • Infeld, L. and Plebansky, J. (1960).Motion and Relativity. Pergamon Press, New York.

    Google Scholar 

  • Iskraut, R. (1942).Zeitschrift für Physik,119, 659.

    Google Scholar 

  • Klark, G. L. (1947).Proceedings of the Royal Society of Edinburgh,62, 412.

    Google Scholar 

  • Klein, F. (1917).Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 469.

  • Klein, F. (1918).Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 171.

  • Klein, F. (1918).Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, Math.-Phys. Klasse, 394.

  • Komar, A. (1963).Physical Review,129, 1873.

    Google Scholar 

  • Kuchar, K. and Langer, J. (1963).Czechoslovak Journal of Physics,B13, 233.

    Google Scholar 

  • Lanczos, K. (1923).Physikalische Zeitschrift,23, 537.

    Google Scholar 

  • Langer, J. (1963).Czechoslovak Journal of Physics,B13, 789.

    Google Scholar 

  • Lopez, C. A. (1965).Nuovo Cimento,A40, 19.

    Google Scholar 

  • Lorentz, H. A. (1915).Verslagen van de gowone vergadering der wis-en natuurkundige afdeeling. K. Akademie van Wetenschappen te Amsterdam,23, 1073.

    Google Scholar 

  • Lorentz, H. A. (1961a).Verslagen van de gowone vergadering der wis- en natuurkundige afdeeling. K. Akademie van Wetenschappen te Amsterdam,24, 1389.

    Google Scholar 

  • Lorentz, H. A. (1916b).Verslagen van de gowone vergadering der wis- en natuurkundige afdeeling. K. Akademie van Wetenschappen te Amsterdam,24, 1759.

    Google Scholar 

  • Lorentz, H. A. (1916c).Verslagen van de gewone vergadering der wis- en natuurkundige afdeeling. K. Akademie van Wetenschappen te Amsterdam,25, 468.

    Google Scholar 

  • Lorentz, H. A. (1916d).Verslagen van de gewone vergadering der wis- en natuurkundige afdeeling. K. Akademie van Wetenschappen te Amsterdam,25, 1380.

    Google Scholar 

  • Misner, C. W. (1963).Physical Review,130, 1590.

    Google Scholar 

  • Mitskevich, N. V. (1958).Annalen der Physik,1, 319.

    Google Scholar 

  • Møller, C. (1958a).Annals of Physics,4, 347.

    Google Scholar 

  • Møller, C. (1958b). InMax-Planck Festschrift, p. 139. Berlin.

  • Møller, C. (1959).Kongelige Danske Videnskabernes Selskabs, Matematisk-fysiske (Meddelelser),31, 14.

    Google Scholar 

  • Møller, C. (1961).Annals of Physics,12, 118.

    Google Scholar 

  • Møller, C. (1964). InAtti del convegno sulla relativita generale: problemi dell energia e ondre gravitazionalli, Vol. 2. Roma.

  • Morgan, T. A. and Joseph, D. W. (1965).Nuovo Cimento,39, 494.

    Google Scholar 

  • Newman, E. T. and Unti, T. W. J. (1962).Journal of Mathematical Physics,3, 891.

    Google Scholar 

  • Nordstrom, G. (1918).Proceedings K. Nederlandse Academie van Wetenschappen Amsterdam,20, 1076.

    Google Scholar 

  • Papapetrou, A. (1947).Proceedings of the Royal Irish Academy,A51, 191.

    Google Scholar 

  • Pauli, W. (1921). Relativitatstheorie.Encyklopadie der Mathematik Wissenschaften,2, 539.

    Google Scholar 

  • Pauli, W. (1941).Review of Modern Physics,13, 203.

    Google Scholar 

  • Penrose, R. (1968).Structure of Space-Time. W. A. Benjamin, Inc., New York.

    Google Scholar 

  • Peres, A. (1959).Nuovo Cimento,11, 644.

    Google Scholar 

  • Petrov, A. Z., Piragas, K. A. and Dobrovolsky, V. A. (1968). InGravitation and Relativity, No. 4–5, p. 44. University Publishing House, Kazan.

    Google Scholar 

  • Pirani, F. A. E. (1961). InGravitation: Introduction to Current Research. Wiley, New York.

    Google Scholar 

  • Plybon, B. (1971).Journal of Mathematical Physics,12, 57.

    Google Scholar 

  • Ray, J. R. (1968).Nuovo Cimento,A56, 189.

    Google Scholar 

  • Rosen, N. (1956). InJubilee of Relativity Theory, p. 170. Birkhauser Verlag, Basel.

    Google Scholar 

  • Rotenberg, M. A. (1972).Journal of Physics A,5, 198.

    Google Scholar 

  • Scahs, R. K. (1962).Proceedings of the Royal Society,270, 102.

    Google Scholar 

  • Schrödinger, E. (1918).Physikalische Zeitschrift,19, 4.

    Google Scholar 

  • Schrödinger, E. (1948).Proceedings of the Royal Irish Academy,A52, 1.

    Google Scholar 

  • Schrödinger, E. (1951).Proceedings of the Royal Irish Academy,A54, 79.

    Google Scholar 

  • Sexl, R. U. (1966).Physics Letters,20, 376.

    Google Scholar 

  • Sheidegger, A. E. (1951).Physical Review,82, 833.

    Google Scholar 

  • Scheidegger, A. E. (1953).Review of Modern Physics,25, 451.

    Google Scholar 

  • Sheidegger, A. E. (1955).Physical Review,99, 1883.

    Google Scholar 

  • Shirokov, M. F. (1972a). InGravitation. Publishing House ‘Naukova Dumka’, Kiev.

    Google Scholar 

  • Shirokov, M. F. (1972b). Institute of Theoretical Physics Preprint, ITP-72-131E, Kiev.

  • Tamburino, L. A. and Winicour, J. H. (1966).Physical Review,150, 1039.

    Google Scholar 

  • Tolman, R. C. (1930).Physical Review,35, 875.

    Google Scholar 

  • Tolman, R. C. (1934).Relativity, Thermodynamics and Cosmology. Clarendon Press, Oxford.

    Google Scholar 

  • Trautman, A. (1956).Bulletin de l'Académie Polonaise des Sciences,4, 665.

    Google Scholar 

  • Trautman, A. (1958).Bulletin de l'Académie Polonaise des Sciences,6, 627.

    Google Scholar 

  • Trautman, A. (1958b). InLectures on General Relativity. King's College, London.

    Google Scholar 

  • Trautman, A. (1964) InLectures on General Relativity. Prentice-Hall, New Jersey.

    Google Scholar 

  • Weber, J. and Wheeler, J. (1957).Review of Modern Physics,29, 509.

    Google Scholar 

  • Weyl, H. (1917).Annalen der Physik,54, 117.

    Google Scholar 

  • Weyl, H. (1918).Raum-Zeit-Materie. Springer Verlag, Berlin.

    Google Scholar 

  • Whittaker, E. T. (1935).Proceedings of the Royal Society,149, 384.

    Google Scholar 

  • Zatzkis, H. (1951).Physical Review,81, 1023.

    Google Scholar 

Download references

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  1. Institute of High Energy Physics, Serpukhov, Moscow District, USSR

    V. N. Folomeshkin

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Folomeshkin, V.N. Zero value of the Schwarzschild mass for an asymptotically Euclidian system of gravitational waves. Int J Theor Phys 11, 387–394 (1974). https://doi.org/10.1007/BF01809717

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  • DOI: https://doi.org/10.1007/BF01809717

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