Skip to main content

Cosmological Singularities

  • Chapter
  • First Online:
Cosmological Crossroads

Part of the book series: Lecture Notes in Physics ((LNP,volume 592))

Abstract

An overview is provided of the singularity theorems in cosmological contexts at a level suitable for advanced graduate students. The necessary background from tensor and causal geometry to understand the theorems is supplied, the mathematical notion of a cosmology is described in some detail and issues related to the range of validity of general relativity are also discussed.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. G.W. Gibbons and S.W. Hawking (eds.): Euclidean Quantum Gravity, (World Scientific, 1993).

    Google Scholar 

  2. R. Penrose: The Emperor’s New Mind, (Oxford University Press, 1989).

    Google Scholar 

  3. D. Kastler (ed.): Quantum Groups, Non-Commutative Geometry and Fundamental Physical Interactions, (Nova Science Publishers, 1999); see also, D. Kastler: Cyclic Cohomology within the Differential Envelope, (Herman, Paris, 1988).

    Google Scholar 

  4. S. Albeverio, J. Jost, S. Paycha and S. Scarlatti: A Mathematical Introduction to String Theory, (LNM225, Cambridge University Press, 1997).

    Google Scholar 

  5. R. Penrose: Singularities and Time-Asymmetry. In: General Relativity: An Einstein Centenary Survey, S.W. Hawking and W. Israel (eds.), (Cambridge University Press, 1979).

    Google Scholar 

  6. J.D. Barrow and S. Cotsakis: Phys.Lett. B214 (1988) 515–518.

    ADS  MathSciNet  Google Scholar 

  7. K. Maeda: Phys.Rev. D39 (1989) 3159.

    ADS  Google Scholar 

  8. S. Cotsakis and J. Miritzis: A Note on Wavemap-Tensor Cosmologies, gr-qc/0107100.

    Google Scholar 

  9. S. Cotsakis: Current Trends in Mathematical Cosmology, gr-qc/0107090.

    Google Scholar 

  10. C.W. Misner, K.S. Thorne and J.A. Wheeler: Gravitation, (Freeman, 1973), Parts III, IV and VII.

    Google Scholar 

  11. R. Penrose: Techniques of Differential Topology in Relativity (SIAM, 1972).

    Google Scholar 

  12. S.W. Hawking and G.F.R. Ellis: The Large Scale Structure of Space-Time (Cambridge University Press, 1973).

    Google Scholar 

  13. Y. Choquet-Bruhat, C. DeWitt-Morette and M. Dillard-Bleick: Analysis, Manifolds and Physics: Basic Theory (North Holland, 2nd ed., 1982).

    Google Scholar 

  14. B. O’Neill: Semi-Riemannian Geometry, (Academic Press, 1983).

    Google Scholar 

  15. R. Penrose, and W. Rindler: Spinors and Space-Time, Volume I, (Cambridge University Press, 1984).

    Google Scholar 

  16. R.M. Wald: General Relativity, (Chicago University Press, 1984).

    Google Scholar 

  17. J.K. Beem, P.E. Ehrlich and K.L. Easley: Global Lorentzian Geometry, (Dekker, 2nd ed., 1996).

    Google Scholar 

  18. M. Kriele: Space-time, (Springer, 1999).

    Google Scholar 

  19. Y. Choquet-Bruhat, C. DeWitt-Morette: Analysis, Manifolds and Physics: Applications (North Holland, 2nd ed., 2000).

    Google Scholar 

  20. R. Geroch: J.Math.Phys. 11 (1970) 437–49.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. R. Penrose: Phys.Rev.Lett. 14 (1965) 57–9.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. S.W. Hawking: Phys.Rev.Lett. 15 (1965) 689–90.

    Article  ADS  MathSciNet  Google Scholar 

  23. S.W. Hawking: Proc.Roy.Soc.Lond. A294 (1966) 511–21.

    ADS  MathSciNet  Google Scholar 

  24. S.W. Hawking: Proc.Roy.Soc.Lond. A295 (1966) 490–93.

    ADS  MathSciNet  Google Scholar 

  25. R. Geroch: Phys.Rev.Lett. 17 (1966) 445–7.

    Article  MATH  ADS  Google Scholar 

  26. S.W. Hawking: Proc.Roy.Soc.Lond. A300 (1967) 187–201.

    ADS  Google Scholar 

  27. S.W. Hawking and R. Penrose: Proc.Roy.Soc.Lond. A314 (1970) 529–48.

    ADS  MathSciNet  Google Scholar 

  28. D. Christodoulou and S. Klainerman: The Global Nonlinear Stability of the Minkowski Space, (Princeton University Press, 1993).

    Google Scholar 

  29. Y. Choquet-Bruhat and V. Moncrief: Future Global in Time Einsteinian Spacetimes with U(1) Isometry Group, Annales Henri Poincaré (to appear).

    Google Scholar 

  30. Y. Choquet-Bruhat and S. Cotsakis: Global Hyperbolicity and Completeness, J.Geom.Phys. (to appear), gr-qc/0201057.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Cotsakis, S. (2002). Cosmological Singularities. In: Cotsakis, S., Papantonopoulos, E. (eds) Cosmological Crossroads. Lecture Notes in Physics, vol 592. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48025-0_4

Download citation

  • DOI: https://doi.org/10.1007/3-540-48025-0_4

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43778-9

  • Online ISBN: 978-3-540-48025-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics