Skip to main content
SpringerLink
Log in

Isotropic Cosmological Singularities

  • Chapter
  • First Online:
The Conformal Structure of Space-Time

Part of the book series: Lecture Notes in Physics ((LNP,volume 604))

Abstract

An isotropic cosmological singularity is a cosmological singularity which can be removed by conformally-rescaling the metric. In the rescaled metric, the singularity is required to occur on a space-like hypersurface. Thus in particular the conformal structure can be extended through the singularity. One can now study the Cauchy problem for the cosmology with data at the singularity for various matter models. I review previous work on this problem and consider various directions for future research.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
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. K. Anguige, Isotropic cosmological singularities 3: The Cauchy problem for the inhomogeneous conformal Einstein-Vlasov equations, Ann.Phys.(NY) 282 395–419 (2000)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  2. K. Anguige and K.P. Tod, Isotropic cosmological singularities 1: Polytropic perfect fluid spacetimes; 2: the Einstein-Vlasov system Ann.Phys.(NY) 276 294–320 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  3. T.N. Bailey, M.G. Eastwood and A.R. Gover, Thomas’s structure bundle for conformal, projective and related structures, Rocky Mountain Jour. Math. 24 1191–1217 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  4. Y. Choquet-Bruhat, ‘Yang-Mills plasmas’ in Global structure and evolution in general relativity Springer Lecture Notes in Physics 460 ed. by S. Cotsakis and G.W. Gibbons (Springer, Berlin, Heidelberg 1996)

    Chapter  Google Scholar 

  5. Y. Choquet-Bruhat and N. Noutchegueme, Système de Yang-Mills-Vlasov en jauge temporelle, Ann.Inst.H.Poincaré 55 759–787 (1991)

    MATH  MathSciNet  Google Scholar 

  6. C.J.S. Clarke, Local extensions in singular space-times, Comm.Math.Phys. 32 203–214 (1973)

    Article  ADS  Google Scholar 

  7. C.J.S. Clarke, The analysis of space-time singularities Cambridge Lecture Notes in Physics 1 (CUP, Cambridge 1993)

    MATH  Google Scholar 

  8. C.M. Claudel and K.P. Newman, The Cauchy problem for quasi-linear hyperbolic evolution problems with a singularity in the time, Proc.Roy.Soc.Lond. A 454 1073–1107 (1998)

    ADS  MathSciNet  Google Scholar 

  9. S.R. de Groot, W.A. van Leeuwen and Ch.G. van Weert: Relativistic Kinetic Theory (North-Holland Publishing Co, Amsterdam 1980)

    Google Scholar 

  10. H. Friedrich, Twistor connection and normal conformal Cartan connection, Gen.Rel.Grav. 8 303–312 (1977)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. H. Friedrich, Einstein equations and conformal structure: existence of anti-de Sitter-type space-times, J.Geom.Phys. 17 125–184 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  12. H. Friedrich and B.G. Schmidt, Conformal geodesics in general relativity Proc.Roy.Soc.Lond A 414 171–195 (1987)

    ADS  MathSciNet  Google Scholar 

  13. S.W. Goode, Vorticity and isotropic singularities, Gen.Rel.Grav. 19 1075–1082 (1987)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  14. S.W. Goode and J. Wainwright, Isotropic singularities in cosmological models, Class.Quant.Grav. 2 99–115 (1985)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. R.P.A.C. Newman, Conformal singularities and the Weyl curvature hypothesis, Rend.Sem.Mat.Univ.Pol.Tor. 50 61–67 (1992)

    MATH  Google Scholar 

  16. R.P.A.C. Newman, On the structure of conformal singularities in classical general relativity: 1 and 2, Proc.Roy.Soc.Lond. A 443 473–492 and 493–515 (1993)

    ADS  Google Scholar 

  17. R. Penrose, ‘Singularities and time-asymmetry’ in: General Relativity and Gravitation: an Einstein centennial volume ed. by W. Israel and S.W. Hawking (CUP, Cambridge 1979)

    Google Scholar 

  18. R. Penrose: The Emperor’s New Mind (OUP, Oxford 1989)

    Google Scholar 

  19. R. Penrose and W. Rindler: Spinors and space-time 2: spinor and twistor methods in space-time geometry (CUP, Cambridge 1986)

    MATH  Google Scholar 

  20. I. Racz, Space-time extensions I, J. Math. Phys. 34 2448–2464 (1993)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. A. Rendall: private communication.

    Google Scholar 

  22. B.G. Schmidt, A new definition of singular points in general relativity, Gen.Rel.Grav. 1 269–280 (1971)

    Article  MATH  ADS  Google Scholar 

  23. B.G. Schmidt, A new definition of conformal and projective infinity of space-times, Comm.Math.Phys. 36 73–90 (1974)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. K.P. Tod, Isotropic singularities and the γ = 2 equation of state, Class.Quant.Grav. 7 L13–L16 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  25. K.P. Tod, Isotropic singularities and the polytropic equation of state, Class.Quant.Grav. 8 L77–L82 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  26. K.P. Tod, Isotropic singularities, Rend.Sem.Mat.Univ.Pol.Tor. 50 69–92 (1992)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Mathematical Institute, Oxford

    K. Paul Tod

Authors
  1. K. Paul Tod
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Theoretische Astrophysik, Universität Tübingen, Auf der Morgenstelle 10, 72076, Tübingen, Germany

    Jörg Frauendiener

  2. MPI für Gravitationsphysik, Albert-Einstein-Institut, Am Mühlenberg 1, 14476, Golm, Germany

    Helmut Friedrich

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Paul Tod, K. (2002). Isotropic Cosmological Singularities. In: Frauendiener, J., Friedrich, H. (eds) The Conformal Structure of Space-Time. Lecture Notes in Physics, vol 604. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45818-2_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-45818-2_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-44280-6

  • Online ISBN: 978-3-540-45818-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation