Communications in Mathematical Physics

, Volume 13, Issue 3, pp 180–193 | Cite as

Limits of spacetimes

  • Robert Geroch
Article

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.

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Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Robert Geroch
    • 1
  1. 1.Department of MathematicsBirkbeck CollegeLondonEngland
  2. 2.Department of PhysicsSyracuse UniversitySyracuse

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