Advertisement

Obtaining analytical approximations to black hole solutions in higher-derivative gravity using the homotopy analysis method

  • Joseph SultanaEmail author
Regular Article

Abstract.

The Homotopy Analysis Method (HAM) is considered as a very useful method for obtaining analytical approximate solutions to various nonlinear differential equations arising in many different areas of science and engineering. Despite this, it is seldom used to obtain solutions in General Relativity and particularly higher order theories of gravity, where due to the complexity and nonlinearity of the field equations, most of the known solutions are numerical. We consider the case of a non-Schwarzschild static and spherically symmetric black hole solution in higher derivative gravity that has been studied recently. We obtain an analytical approximation using HAM and compare it with the numerical solution.

References

  1. 1.
    M. Hermann, M. Saravi, Nonlinear Ordinary Differential Equations: Analytical Approximations and Numerical Methods (Springer-Verlag, India, 2016)Google Scholar
  2. 2.
    S.J. Liao, Beyond perturbation: Introduction to the Homotopy Analysis Method (Chapman & Hall/CRC Press, Boca Raton, 2003)Google Scholar
  3. 3.
    S.J. Liao, On the proposed homotopy analysis techniques for nonlinear problems and its application, PhD dissertation, Shanghai Jiao Tong University, 1992Google Scholar
  4. 4.
    S.J. Liao, Int. J. Nonlinear Mech. 34, 759 (1999)ADSCrossRefGoogle Scholar
  5. 5.
    S.J. Liao, Appl. Math. Comput. 147, 499 (2004)MathSciNetGoogle Scholar
  6. 6.
    S.J. Liao, Stud. Appl. Math. 119, 297 (2007)MathSciNetCrossRefGoogle Scholar
  7. 7.
    S.J. Liao, Commun. Nonlinear Sci. Numer. Simul. 14, 983 (2009)ADSMathSciNetCrossRefGoogle Scholar
  8. 8.
    R.A. Van Gorder, K. Vajravelu, Phys. Lett. A 372, 6060 (2008)ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    S. Abbanbandy, Appl. Math. Model. 32, 2706 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    M. Sajiad, T. Hayat, Nonlinear Anal. Real World Appl. 9, 2296 (2008)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Y.M. Chen, J.K., Commun. Nonlinear Sci. Numer. Simul. 14, 1861 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    H. Jafari, S. Seifi, Commun. Nonlinear Sci. Numer. Simul. 14, 2006 (2009)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    AK. Alomari, M.S.M. Noorani, R. Nazar, Commun. Nonlinear Sci. Numer. Simul. 14, 1196 (2009)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    G. Domairry, M. Fazeli, Commun. Nonlinear Sci. Numer. Simul. 14, 489 (2009)ADSCrossRefGoogle Scholar
  15. 15.
    A. Sami Bataineh, M.S.M. Noorani, I. Hashim, Comput. Math. Appl. 55, 2913 (2008)MathSciNetCrossRefGoogle Scholar
  16. 16.
    K. Yabushita, M. Yamashita, K. Tsuboi, Phys. A Math. Theor. 40, 84036 (2007)Google Scholar
  17. 17.
    A. Sami Bataineh, M.S.M. Noorani, I. Hashim, Commun. Nonlinear Sci. Num. Simul. 13, 2060 (2008)CrossRefGoogle Scholar
  18. 18.
    M. Turkyilmazoglu, Filomat 31, 2633 (2017)MathSciNetCrossRefGoogle Scholar
  19. 19.
    R.A. Van Gorder, Numer. Algor. 76, 151 (2017)CrossRefGoogle Scholar
  20. 20.
    H.N. Hassan, M.A. El-Tawil, Math. Meth. Appl. Sci. 34, 728 (2011)CrossRefGoogle Scholar
  21. 21.
    R.A. Van Gorder, K. Vajravelu, Commun. Nonlinear Sci. Numer. Simulat. 14, 4078 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Yinshan, T. Chaolu, in 2010 International Conference on Intelligent Computing and Integrated Systems (2010)  https://doi.org/10.1109/ICISS.2010.5656089
  23. 23.
    H. Lü, A. Perkins, C.N. Pope, K.S. Stelle, Phys. Rev. Lett. 114, 171601 (2015)ADSCrossRefGoogle Scholar
  24. 24.
    K. Kokkotas, R.A. Konoplya, A. Zhidenko, Phys. Rev. D 96, 064007 (2017)ADSMathSciNetCrossRefGoogle Scholar
  25. 25.
    W. Nelson, Phys. Rev. D 82, 104026 (2010)ADSCrossRefGoogle Scholar
  26. 26.
    J.H. He, Appl. Math. Comput. 135, 73 (2003)MathSciNetGoogle Scholar
  27. 27.
    S. Liao, Appl. Math. Comput. 169, 1186 (2005)MathSciNetGoogle Scholar
  28. 28.
    A. Sami Bataineh, M.S.M. Noorani, I. Hashim, Commun. Nonlinear Sci. Numer. Simulat. 14, 430 (2009)ADSCrossRefGoogle Scholar
  29. 29.
    R.A. Van Gorder, arXiv:1606.02644Google Scholar
  30. 30.
    L. Rezzolla, A. Zhidenko, Phys. Rev. D 90, 084009 (2014)ADSCrossRefGoogle Scholar
  31. 31.
    R. Konoplya, L. Rezzolla, A. Zhidenko, Phys. Rev. D 93, 064015 (2016)ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceUniversity of MaltaMsidaMalta

Personalised recommendations