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A numerical sufficient condition for deciding if a space-time is inextendible

Численное достаточное условие для определения, является ли пространство-время нерастяжимым

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Il Nuovo Cimento B (1971-1996)

Summary

A sufficient condition for the inextendibility of a space-time is presented based upon the notion of a «tangent space» at the boundary of the space-time.

Riassunto

Si presenta una condizione sufficiente per la non estendibilità di uno spazio-tempo basata sulla nozione di «spazio tangente» al limite dello spazio-tempo.

Резюме

Предлагается достаточное условие для нерастяжимости пространства-времени, которое основано на представлении «касательного пространства» на границе пространства-времени.

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References

  1. A space-timeM is a connected Hausdorff 4-dimensional manifold with aC ∞ metric of signature (−−, −, +). We assumeM is orientable and time-orientable.M is said to be extendible if it is isometric to a proper subset of some other space-time; other-wiseM is said to be maximal or inextendible.

  2. C. W. Misner:Journ. Math. Phys.,4, 924 (1963).

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  3. B. Schmidt:Gen. Rel. Grav.,1, 269 (1971).

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  4. R. Geroch:Ann. of Phys.,48, 526 (1968).

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  5. L(M) is a special case of a principal fibre bundle; seeS. Kobayashi andK. Nomizu:Foundations of Differential Geometry, Vol.1 (New York, N. Y., 1963). Our procedure is a special case of construction of a bundle associated with a general fibre bundle.

  6. P. Hajicek andB. Schmidt:Comm. Math. Phys.,23, 285 (1971).

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Author information

Author notes

  1. D. P. Duncan

    Present address: Bell Laboratories, 07974, Murray Hill, N.J.

Authors and Affiliations

  1. Center for Relativity, The University of Texas at Austin, Austin, Tex.

    D. P. Duncan & L. C. Shepley

Authors
  1. D. P. Duncan
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  2. L. C. Shepley
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Additional information

Traduzione a cura della Redazine.

Переведено редакцией.

Work supported in part by NSF-USDP Grant GU-1598 and NSF Grants GP-34639X-1 and GP-32039.

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Duncan, D.P., Shepley, L.C. A numerical sufficient condition for deciding if a space-time is inextendible. Nuov Cim B 24, 130–134 (1974). https://doi.org/10.1007/BF02724038

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  • DOI: https://doi.org/10.1007/BF02724038

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