Skip to main content
Log in

Limits of spacetimes

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript


The limits of a one-parameter family of spacetimes are defined, and the properties of such limits discussed. The definition is applied to an investigation of the Schwarzschild solution as a limit of the Reissner-Nordström solution as the charge parameter goes to zero. Two new techniques — rigidity of a geometrical structure and Killing transport — are introduced. Several applications of these two subjects, both to limits and to certain other questions in differential geometry, are discussed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others


  1. Kasner, E.: Am. J. Math.43, 217 (1921).

    Google Scholar 

  2. Penrose, R.: Ann. Phys. (N.Y.)10, 171 (1960).

    Google Scholar 

  3. Penrose, R., W. Rindler, andR. Geroch: The spinor approach to space-time. Cambridge: University Press (to be published).

  4. Geroch, R.: J. Math. Phys.9, 1739 (1968);

    Google Scholar 

  5. -- The spinor structure of space-times in general relativity II. J. Math. Phys. (to be published).

  6. Penrose, R.: Phys. Rev. Letters14, 57 (1965).

    Google Scholar 

  7. Geroch, R.: The domain of dependence. J. Math. Phys. to be published.

  8. Penrose, R.: Proc. Roy. Soc. A284, 159 (1965).

    Google Scholar 

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

    Google Scholar 

  10. Synge, J. L., Relativity: The general theory, pp. 310. Amsterdam: North-Holland Publ. Co. 1960.

    Google Scholar 

  11. Haantjes, J.: article in: International Conference on Differential Geometry, Rome, 1953, pp. 77. Edizioni Cremonese della Casa Editrice Parrella Roma 1954.

  12. Ref. 9, pp. 278.

    Google Scholar 

  13. Schouten, J. A.: Ricci Calculus, pp. 306. Berlin-Heidelberg: Springer 1954.

    Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

About this article

Cite this article

Geroch, R. Limits of spacetimes. Commun.Math. Phys. 13, 180–193 (1969).

Download citation

  • Received:

  • Issue Date:

  • DOI: