Advertisement

Exploring Levi-Civita’s cylindrical solutions in \(f(\mathcal{G},T)\) gravity

  • Mushtaq Ahmad
  • M. Farasat ShamirEmail author
Original Article
  • 48 Downloads

Abstract

An exact solution pertaining to the existence of cosmic strings has been discussed for a cylindrically symmetric \(f(\mathcal{G},T)\) gravity model, with \(\mathcal{G}\) being the Gauss-Bonnet invariant and \(T\) the trace of energy momentum tensor. This solution corresponds to the generalised vacuum Levi-Civita’s metric in general relativity. Exclusive expressions for the energy density and pressure terms along with their corresponding null energy constraints have been worked out and analyzed graphically. It has been shown that the energy density remains positive and the null energy conditions are met largely for some particular choices of the parametric terms appearing in the model. However, certain violation of these energy constraints under specific circumstances hints the existence of cylindrical wormholes. Moreover, if the coupling constant of the Gauss-Bonnet invariant is set to null, Levi-Civita vacuum solution in general relativity is recovered.

Keywords

\(f(\mathcal{G},T)\) gravity Cosmic Strings Levi-Civita’s Solution 

Notes

Acknowledgements

Many thanks to the anonymous reviewers for valuable comments and suggestions to improve the paper. This work was supported by National University of Computer and Emerging Sciences (NUCES), Pakistan.

References

  1. Aryal, M., Ford, L.H., Vilenkin, A.: Phys. Rev. D 34, 2263 (1986) ADSMathSciNetCrossRefGoogle Scholar
  2. Azadi, A., Momeni, D., Nouri-Zonoz, M.: Phys. Lett. B 670, 210 (2008) ADSMathSciNetCrossRefGoogle Scholar
  3. Berkeley, J., Berman, D.S.: J. High Energy Phys. 2013, 92 (2013) CrossRefGoogle Scholar
  4. Buchdahl, H.A.: Phys. Rev. 115, 1325 (1959) ADSMathSciNetCrossRefGoogle Scholar
  5. Camci, U.: Eur. Phys. J. C 74, 3201 (2014a) ADSCrossRefGoogle Scholar
  6. Camci, U.: J. Cosmol. Astropart. Phys. 07, 002 (2014b) ADSCrossRefGoogle Scholar
  7. Chiba, T.: J. Cosmol. Astropart. Phys. 03, 008 (2005) ADSCrossRefGoogle Scholar
  8. Cognola, G., Elizalde, E., Nojiri, S., Odintsov, S.D., Zerbini, S.: Phys. Rev. D 75, 086002 (2007) ADSMathSciNetCrossRefGoogle Scholar
  9. Cognola, G., Gastaldi, M., Zerbini, S.: Int. J. Theor. Phys. 47, 898 (2008) CrossRefGoogle Scholar
  10. De Felice, A., Tsujikawa, S.: Phys. Lett. B 675, 1 (2009) ADSCrossRefGoogle Scholar
  11. Ehlers, J.: In: Colloques Internationaux CNRS (Les theories relativistes de la gravitation) vol. 91, p. 275 (1962) Google Scholar
  12. Elizalde, E., Myrzakulov, R., Obukhov, V.V., Sez-Gmez, D.: Class. Quantum Gravity 27, 095007 (2010) ADSCrossRefGoogle Scholar
  13. Felice, A.D., Suyama, T., Tanaka, T.: Phys. Rev. D 83, 104035 (2011) ADSCrossRefGoogle Scholar
  14. Gleiser, M.A., Clement, G.: Class. Quantum Gravity 13, 2635 (1996) ADSCrossRefGoogle Scholar
  15. Gleiser, R.J., Tiglio, M.H.: Phys. Rev. D 58, 124028 (1998) ADSCrossRefGoogle Scholar
  16. Houndjo, M.J.S., Rodrigues, M.E., Momeni, D., Myrzakulov, R.: Can. J. Phys. 92, 1528 (2014) ADSCrossRefGoogle Scholar
  17. Israel, Q., Eduardo, T.: (2010). arXiv:1005.2600 [gr-qc]
  18. Khoeini-Moghaddam, S., Nouri-Zonoz, M.: Phys. Rev. D 72, 064004 (2005) ADSMathSciNetCrossRefGoogle Scholar
  19. Klepac, P., Horsky, J.: Gen. Relativ. Gravit. 34, 1979 (2002) CrossRefGoogle Scholar
  20. Laurentis, M., Paolella, M., Capozziello, S.: Phys. Rev. D 91, 083531 (2015) ADSMathSciNetCrossRefGoogle Scholar
  21. Levi-Civita, T.: Rend. Accad. Lincei 27, 183 (1917) Google Scholar
  22. Momeni, D., Gholizade, H.: Int. J. Mod. Phys. D 18, 1719 (2009) ADSCrossRefGoogle Scholar
  23. Myrzakulov, R., Sez-Gmez, D., Tureanu, A.: Gen. Relativ. Gravit. 43, 1671 (2011) ADSCrossRefGoogle Scholar
  24. Nojiri, S., Odintsov, S.D.: Phys. Lett. B 631, 1 (2005) ADSMathSciNetCrossRefGoogle Scholar
  25. Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011) ADSMathSciNetCrossRefGoogle Scholar
  26. Nojiri, S., Odintsov, S.D., Tretyakov, P.V.: Prog. Theor. Phys. Suppl. 172, 81 (2008) ADSCrossRefGoogle Scholar
  27. Pani, P., Sotiriou, T.P., Vernieri, D.: Phys. Rev. D 88, 121502 (2013) ADSCrossRefGoogle Scholar
  28. Rodrigues, M.E., Houndjo, M.J.S., Momeni, D., Myrzakulov, R.: Can. J. Phys. 92, 173 (2014) ADSCrossRefGoogle Scholar
  29. Said, J.L., Sultana, J., Zarb Adami, K.: Phys. Rev. D 85, 104054 (2012) ADSCrossRefGoogle Scholar
  30. Sebastiani, L.: Springer Proceedings in Physics, vol. 137, p. 261 (2011) zbMATHGoogle Scholar
  31. Shamir, M.F.: Astrophys. Space Sci. 361, 147 (2016a) ADSCrossRefGoogle Scholar
  32. Shamir, M.F.: J. Exp. Theor. Phys. 123, 607 (2016b) ADSCrossRefGoogle Scholar
  33. Sharif, M., Fatima, H.I.: Int. J. Mod. Phys. D 25, 1650011 (2016) ADSCrossRefGoogle Scholar
  34. Sharif, M., Ikram, A.: J. Exp. Theor. Phys. 123, 40 (2016) ADSCrossRefGoogle Scholar
  35. Stephani, H., Kramer, D., MacCallum, M., Hoenselaers, C., Herlt, E.: Exact Solutions of Einsteins Field Equations, 2nd edn. p. 6. Cambridge University Press, Cambridge (2003) CrossRefGoogle Scholar
  36. Tsujikawa, S.: Lect. Notes Phys., vol. 800 (2010) Google Scholar
  37. Wu, B., Ma, B.: Phys. Rev. D 92, 044012 (2015) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.National University of Computer and Emerging SciencesLahore CampusPakistan

Personalised recommendations