Relativistic Burgers Models on Curved Background Geometries

  • Baver OkutmusturEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)


Relativistic Burgers model and its generalization to various spacetime geometries are recently studied both theoretically and numerically. The numeric implementation is based on finite volume and finite difference approximation techniques designed for the corresponding model on the related geometry. In this work, we provide a summary of several versions of these models on the Schwarzschild, de Sitter, Schwarzschild-de Sitter, FLRW and Reissner-Nordström spacetime geometries with their particular properties.



Supported by METU-GAP Project, Project no: GAP-101-2018-2767.


  1. 1.
    Amorim, P., LeFloch, P.G., Okutmustur, B.: Finite volume schemes on Lorentzian manifolds. Commun. Math. Sci. 6(4), 1059–1086 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Ceylan, T., Okutmustur, B.: Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime. Turk. J. Math. 41, 1027–1041 (2017)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Ceylan, T., Okutmustur, B.: Finite volume method for the relativistic Burgers model on a (1+1)-dimensional de Sitter spacetime. Math. Comput. Appl. 21(2), 16 (2016)MathSciNetGoogle Scholar
  4. 4.
    Ceylan, T., LeFloch, P.G., Okutmustur, B.: A finite volume method for the relativistic Burgers equation on a FLRW background spacetime. Commun. Comput. Phys. 23, 500–519 (2018)MathSciNetCrossRefGoogle Scholar
  5. 5.
    LeFloch, P.G., Makhlof, H., Okutmustur, B.: Relativistic Burgers equations on a curved spacetime. Derivation and finite volume approximation. SIAM J. Numer. Anal. 50(4), 2136–2158 (2012)MathSciNetCrossRefGoogle Scholar
  6. 6.
    LeFloch, P.G., Okutmustur, B.: Hyperbolic conservation laws on spacetimes. A finite volume scheme based on differential forms. Far East J. Math. Sci. 31, 49–83 (2008)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Nordebo, J.: The Reissner-Nordström metric. M.S. Dissertion, Department of Physics, Umea University, Switzerland (2016)Google Scholar
  8. 8.
    LeVeque, R.J.: Finite Volume Methods for Hyperbolic Problems, 1st edn. Cambridge University Press, Cambridge (2002)CrossRefGoogle Scholar
  9. 9.
    Nashed, G.G.L.: Stability of Reissner-Nordström black hole. Acta Phys. Pol. 112, 13–19 (2007)CrossRefGoogle Scholar
  10. 10.
    Okutmustur, B.: Propagations of shock and rarefaction waves on the Reissner-Nordström spacetimes for Burgers models. SDU J. Nat. Appl. Sci. 22(Spec. Issue), 448–459 (2018)Google Scholar
  11. 11.
    Wald, R.M.: General Relativity, 1st edn. The University of Chicago Press, Chicago (1984)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical University (METU)AnkaraTurkey

Personalised recommendations