Communications in Mathematical Physics

, Volume 46, Issue 2, pp 135–152 | Cite as

An application of Morse theory to space-time geometry

  • N. M. J. Woodhouse


Milnor's treatment [6] of Morse's global theory of the calculus of variations for geodesics [7] is restated in the context of space-time geometry: it is seen as providing a link between the curvature and the causal structure of a stably causal globally hyperbolic Lorentzian manifold. An application is discussed.


Neural Network Manifold Statistical Physic Complex System Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Greenberg, M.J.: Lectures on algebraic topology. Menlo Park, California: Benjamin 1966Google Scholar
  2. 2.
    Hawking, S.W.: Proc. Roy. Soc. A308, 433 (1968)Google Scholar
  3. 3.
    Hawking, S.W.: The event horizon. In: DeWitt, C., DeWitt, B.S. (Eds.): Les astres occlus, les Houches 1972. New York-London-Paris: Gordon and Breach 1973Google Scholar
  4. 4.
    Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. Cambridge: University Press 1973Google Scholar
  5. 5.
    Kronheimer, E.H.: G.R.G.1, 261 (1971)Google Scholar
  6. 6.
    Milnor, J.: Morse theory, annals of mathematics studies 51. Princeton: University Press 1963Google Scholar
  7. 7.
    Morse, M.: The calculus of variations in the large. New York: American Mathematical Society 1934Google Scholar
  8. 8.
    Palais, R.S.: Topology2, 299 (1963)Google Scholar
  9. 9.
    Penrose, R.: Techniques of differential topology in relativity. Philadelphia: SIAM 1974Google Scholar
  10. 10.
    Penrose, R.: Lectures at IAU symposia Nos. 63 and 64 (Warsaw, Cracow 1973) (to be published in the proceedings of the conference)Google Scholar
  11. 11.
    Pirani, F.A.E.: Introduction to gravitational radiation theory. In: Lectures on general relativity, Brandeis Summer Institute 1964. Englewood Cliffs, New Jersey: Prentice-Hall 1965Google Scholar
  12. 12.
    Smale, S.: Ann. Math.80, 382 (1964)Google Scholar
  13. 13.
    Smith, J.W.: Proc. Nat. Acad. Sci.46, 111 (1960)Google Scholar
  14. 14.
    Smith, J.W.: Amer. J. Math.82, 873 (1961)Google Scholar
  15. 15.
    Woodhouse, N.M.J.: Causal spaces and the structure of space-time. Thesis, London University 1973Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • N. M. J. Woodhouse
    • 1
  1. 1.Department of MathematicsUniversity of London, King's CollegeLondonEngland

Personalised recommendations