Skip to main content
SpringerLink
Log in

Modelling inhomogeneity in Szekeres spacetime

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

We study the behaviour of the density contrast in quasi-spherical Szekeres spacetime and derive its analytical behaviour as a function of \(t\) and \(r\). We set up the inhomogeneity using initial data in the form of one extreme value of the density and the radial profile. We derive conditions for density extremes that are necessary for avoiding the shell crossing singularity and show that in the special case of a trivial curvature function, the conditions are preserved by evolution. We also show that in this special case if the initial inhomogeneity is small, the time evolution does not influence the density contrast, however its magnitude homogeneously decreases.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Lemaitre, G.: L’Univers en expansion. Ann. Soc. Sci. Bruxelles A 53, 51–85 (1933)

    ADS  Google Scholar 

  2. Szekeres, P.: Quasispherical gravitational collapse. Phys. Rev. D 12, 2941–8 (1975)

    Article  ADS  Google Scholar 

  3. Szafron, D.A.: Inhomogeneous cosmologies: New exact solutions and their evolution. J. Math. Phys. 18, 1673 (1975)

    Article  MathSciNet  ADS  Google Scholar 

  4. Stephani, H.: Über Lösungen der Einsteinschen Feldgleichungen, die sich in einen fünfdimensionalen flachen Raum einbetten lassen. Commun. Math. Phys. 4, 137 (1967)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  5. Krasinski, A.: Inhomogeneous Cosmological Models. CUP, Cambridge (1997)

    Book  MATH  Google Scholar 

  6. Krasinski, A., Hellaby, Ch.: Formation of a galaxy with a central black hole in the Lematre-Tolman model. Phys. Rev. D 69, 043502 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  7. Krasinski, A., Hellaby, Ch.: More examples of structure formation in the Lematre-Tolman model. Phys. Rev. D 69, 023502 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  8. Hellaby, Ch., Krasinski, A.: Alternative methods of describing structure formation in the Lemaitre-Tolman model. Phys. Rev. D 73, 023518 (2006)

    Article  ADS  Google Scholar 

  9. Bolejko, K., Krasinski, A., Hellaby, Ch.: Formation of voids in the Universe within the Lemaitre-Tolman model. Mon. Not. Roy. Astron. Soc. 362, 213–228 (2005)

    Article  ADS  Google Scholar 

  10. Hellaby, Ch., Krasinski, A.: You cannot get through Szekeres wormholes: Regularity, topology, and causality in quasispherical Szekeres models. Phys. Rev. D 66, 084011 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  11. Hellaby, Ch., Krasinski, A.: Physical and geometrical interpretation of the Szekeres models. Phys. Rev. D 77, 023529 (2008)

    Article  ADS  Google Scholar 

  12. Krasinski, A.: Geometry and topology of the quasiplane Szekeres model. Phys. Rev. D 78, 064038 (2008); erratum Phys. Rev. D 85, 069903(E) (2012)

  13. Krasinski, A., Bolejko, K.: Geometry of the quasihyperbolic Szekeres models. Phys. Rev. D 86, 104036 (2012)

    Article  ADS  Google Scholar 

  14. Bolejko, K.: Structure formation in the quasispherical Szekeres model. Phys. Rev. D 73, 123508 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  15. Bolejko, K.: Evolution of cosmic structures in different environments in the quasispherical Szekeres model. Phys. Rev. D 75, 043508 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  16. Bolejko, K.: Volume averaging in the quasispherical Szekeres model. Gen. Rel. Grav. 41, 1585–1593 (2009)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  17. Bolejko, K., Celerier, M.N.: Szekeres Swiss-cheese model and supernova observations. Phys. Rev. D 82, 103510 (2010)

    Article  ADS  Google Scholar 

  18. Bolejko, K.: The Szekeres Swiss Cheese model and the CMB observations. Gen. Rel. Grav. 41, 1737–1755 (2009)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  19. Walters, A., Hellaby, Ch.: Constructing Realistic Szekeres Models from Initial and Final Data. JCAP 1212, 001 (2012)

    Article  MathSciNet  ADS  Google Scholar 

  20. Hellaby, Ch.: The nonsimultaneous nature of the Schwarzschild R=0 singularity. J. Math. Phys. 37, 2892–905 (1996)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  21. Berger, B.K., Eardley, D.M., Olson, D.W.: Note on the spacetimes of Szekeres. Phys. Rev. D 16, 3086–9 (1977)

    Article  MathSciNet  ADS  Google Scholar 

  22. Hellaby, Ch.: A Kruskal-Like Model with Finite Density. Class. Quantum Grav. 4, 635–50 (1987)

    Article  MathSciNet  MATH  ADS  Google Scholar 

  23. Sussman, R.: A., Bolejko, K.: A novel approach to the dynamics of Szekeres dust models. Class. Quantum Grav. 29, 065018 (2012)

    Article  MathSciNet  ADS  Google Scholar 

Download references

Acknowledgments

D. V. was supported by Grant GAUK 398911 and project SVV-267301. O. S. was supported by Grant GAČR 14-37086G.

Author information

Authors and Affiliations

  1. Institute of Theoretical Physics, Faculty of Mathematics and Physics, Charles University in Prague, V Holešovičkách 2, 180 00, Prague 8, Czech Republic

    David Vrba & Otakar Svítek

Authors
  1. David Vrba
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Otakar Svítek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Otakar Svítek.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vrba, D., Svítek, O. Modelling inhomogeneity in Szekeres spacetime. Gen Relativ Gravit 46, 1808 (2014). https://doi.org/10.1007/s10714-014-1808-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-014-1808-x

Keywords

Search

Navigation