Abstract
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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Kasner, E.: Am. J. Math.43, 217 (1921).
Penrose, R.: Ann. Phys. (N.Y.)10, 171 (1960).
Penrose, R., W. Rindler, andR. Geroch: The spinor approach to space-time. Cambridge: University Press (to be published).
Geroch, R.: J. Math. Phys.9, 1739 (1968);
-- The spinor structure of space-times in general relativity II. J. Math. Phys. (to be published).
Penrose, R.: Phys. Rev. Letters14, 57 (1965).
Geroch, R.: The domain of dependence. J. Math. Phys. to be published.
Penrose, R.: Proc. Roy. Soc. A284, 159 (1965).
Geroch, R.: Ann. Phys.48, 526 (1968).
Synge, J. L., Relativity: The general theory, pp. 310. Amsterdam: North-Holland Publ. Co. 1960.
Haantjes, J.: article in: International Conference on Differential Geometry, Rome, 1953, pp. 77. Edizioni Cremonese della Casa Editrice Parrella Roma 1954.
Ref. 9, pp. 278.
Schouten, J. A.: Ricci Calculus, pp. 306. Berlin-Heidelberg: Springer 1954.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Geroch, R. Limits of spacetimes. Commun.Math. Phys. 13, 180–193 (1969). https://doi.org/10.1007/BF01645486
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01645486