Skip to main content
SpringerLink
Log in

Poisson type relativistic perfect fluid spheres

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Static spherically symmetric solutions of the Einstein’s field equations in isotropic coordinates representing perfect fluid matter distributions from Newtonian potential–density pairs are investigated. The approach is illustrated with three simple examples based on the potential–density pairs corresponding to a harmonic oscillator (homogeneous sphere), the well-known Plummer model and a massive spherical dark matter halo model with a logarithmic potential. Moreover, the geodesic circular motion of test particles around such structures is studied. The stability of the orbits against radial perturbations is also analyzed using an extension of the Rayleigh criteria of stability of a fluid in rest in a gravitational field. The models considered satisfy all the energy conditions.

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. M.I. Wilkinson, J. Kleyna, N.W. Evans, G. Gilmore, MNRAS 330, 778 (2002)

    Article  ADS  Google Scholar 

  2. A.T. Bajkova, V.V. Bobylev, Astron. Lett. 42(9), 567 (2016)

    Article  ADS  Google Scholar 

  3. V.V. Bobylev, A.T. Bajkova, A.O. Gromov, Astron. Lett. 43(4), 241 (2017)

    Article  ADS  Google Scholar 

  4. W. Dehnen, MNRAS 265, 250 (1993)

    Article  ADS  Google Scholar 

  5. S. Tremaine et al., Astron. J. 107, 634 (1994)

    Article  ADS  Google Scholar 

  6. H.C. Plummer, MNRAS 71, 460 (1911)

    Article  ADS  Google Scholar 

  7. L. Hernquist, Astrophys. J. 356, 359 (1990)

    Article  ADS  Google Scholar 

  8. J.F. Navarro, C.S. Frenk, S.D.M. White, Astrophys. J. 462, 563 (1996)

    Article  ADS  Google Scholar 

  9. M.S.R. Delgaty, K. Lake, Comput. Phys. Commun. 115, 395 (1998)

    Article  ADS  Google Scholar 

  10. H. Stephani, D. Kramer, M. McCallum, C. Hoenselaers, E. Herlt, Exact Solutions of Einsteins’s Field Equations (Cambridge University Press, Cambridge, 2003)

    Book  Google Scholar 

  11. D. Vogt, P.S. Letelier, Mon. Not. R. Astron. Soc. 402, 1313 (2010)

    Article  ADS  Google Scholar 

  12. D. Vogt, P.S. Letelier, Mon. Not. R. Astron. Soc. 406, 2689 (2010)

    Article  ADS  Google Scholar 

  13. P.H. Nguyen, M. Lingam, Mon. Not. R. Astron. Soc. 436(3), 2014 (2013)

    Article  ADS  Google Scholar 

  14. G. García-Reyes, Gen. Relativ. Gravit. 49(3), 1–13 (2017)

    Article  MathSciNet  Google Scholar 

  15. G. García-Reyes, K.A. Hernández-Gómez, Int. J. Mod. Phys. 27(07), 1850068-1 (2018)

    Article  ADS  Google Scholar 

  16. R.C. Tolman, Relativity, Thermodynamics, and Cosmology (Oxford University Press, London, 1934)

    MATH  Google Scholar 

  17. YaB Zeldovich, J.D. Novikov, Relativistic Astrophysics, vol. I: Stars and Relativity (University of Chicago Press, Chicago, 1971)

    Google Scholar 

  18. T. Matos, D. Núñez, R.A. Sussman, Class. Quant. Gravity 21(22), 5275 (2004)

    Article  ADS  Google Scholar 

  19. L.D. Landau, E.M. Lifshitz, Classical Theory of Fields (Pergamon, Oxford, 1976)

    MATH  Google Scholar 

  20. L.D. Landau, E.M. Lifshitz, Fluid Mechanics (Addison-Wesley, Reading, 1989)

    Google Scholar 

  21. A.H. Taub, Ann. Rev. Fluid Mech. 10, 301 (1978)

    Article  ADS  Google Scholar 

  22. J.L. Synge, Relativity: The General Theory (NorthHolland, Amsterdam, 1966)

    MATH  Google Scholar 

  23. C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (Freeman, San Francisco, 1973)

    Google Scholar 

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

    Book  Google Scholar 

  25. B. Schutz, A First Course in General Relativity, 2nd edn. (Cambridge University Press, Cambridge, 2009)

    Book  Google Scholar 

  26. P. Kustaanheimo, B. Qvist, Gen. Relativ. Gravit. 30(4), 663 (1998)

    Article  ADS  Google Scholar 

  27. Lord Rayleigh, Proc. R. Soc. Lond. A 93, 148 (1917)

    Article  ADS  Google Scholar 

  28. P.S. Letelier, Phys. Rev. D 68, 104002 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  29. G. Darmois, Mémorial des Sciences Mathématiques (Gauthier-Villars, Paris, 1927). Fasc. 25

    Google Scholar 

  30. W.B. Bonnor, P.A. Vickers, Gen. Relativ. Gravit. 13(1), 29 (1981)

    Article  ADS  Google Scholar 

  31. M. Miyamoto, R. Nagai, Publ. Astron. Soc. Jpn. 27, 533 (1975)

    ADS  Google Scholar 

  32. R. Nagai, M. Miyamoto, Publ. Astron. Soc. Jpn. 28, 1 (1976)

    ADS  Google Scholar 

  33. H.A. Buchdahl, Astrophys. J. 140, 1512 (1964)

    Article  ADS  MathSciNet  Google Scholar 

  34. J. Binney, Mon. Not. R. Astron. Soc. 196, 455 (1981)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Física, Universidad Tecnológica de Pereira, A. A. 97, Pereira, Colombia

    Gonzalo García-Reyes

Authors
  1. Gonzalo García-Reyes
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gonzalo García-Reyes.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

García-Reyes, G. Poisson type relativistic perfect fluid spheres. Eur. Phys. J. Plus 135, 931 (2020). https://doi.org/10.1140/epjp/s13360-020-00948-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-020-00948-x

Search

Navigation