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Plane Symmetric Solutions in f(\(\mathcal{G}\), T) Gravity

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Abstract

We obtain several exact solutions for a plane symmetric space–time in the framework of a recently constructed f(\(\mathcal{G}\), T) theory of gravity, where f(\(\mathcal{G}\), T) is a generic function of the Gauss–Bonnet invariant G and the trace T of the energy–momentum tensor. To obtain solutions, we consider a power-law f(\(\mathcal{G}\), T) gravity model and analyze the obtained results graphically. Moreover, to justify the method, we reconstruct several well-known cosmological results.

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References

  1. S. Nojiri and S. D. Odintsov, “Modified Gauss–Bonnet theory as gravitational alternative for dark energy,” Phys. Lett. B, 631, 1–6 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. S. Nojiri, S. D. Odintsov, and O. G. Gorbunova, “Dark energy problem: From phantom theory to modified Gauss–Bonnet gravity,” J. Phys. A, 39, 6627–6633 (2006); arXiv:hep-th/0510183v2 (2005).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  3. G. Congnola, E. Elizalde, S. Nojiri, S. D. Odintsov, and S. Zerbini, “Dark energy in modified Gauss–Bonnet gravity: Late-time acceleration and the hierarchy problem,” Phys. Rev. D, 73, 084007 (2006); arXiv:hep-th/0601008v2 (2006)

    Article  ADS  Google Scholar 

  4. “String-inspired Gauss–Bonnet gravity reconstructed from the universe expansion history and yielding the transition from matter dominance to dark energy,” Phys. Rev. D, 75, 086002 (2007); arXiv:hep-th/0611198v3 (2006).

  5. S. M. Carroll, A. De Felice, V. Duvvuri, D. A. Easson, M. Trodden, and M. S. Turner, “Cosmology of generalized modified gravity models,” Phys. Rev. D, 71, 063513 (2005); arXiv:astro-ph/0410031v2 (2004).

    Article  ADS  Google Scholar 

  6. B. M. N. Carter and I. P. Neupane, “Dynamical relaxation of dark energy: A solution to early inflation, latetime acceleration, and the cosmological constant problem,” Phys. Lett. B, 638, 94–99 (2006); arXiv:hep-th/0510109v5 (2005).

    Article  ADS  MATH  Google Scholar 

  7. S. Nojiri and S. D. Odintsov, “Modified f(R) gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe,” Phys. Rev. D, 74, 086005 (2006); arXiv:hep-th/0608008v3 (2006).

    Article  ADS  Google Scholar 

  8. S. Nojiri, S. D. Odintsov, and P. V. Tretyakov, “From inflation to dark energy in the non-minimal modified gravity,” Prog. Theor. Phys. Suppl., 172, 81–89 (2008); arXiv:0710.5232v1 [hep-th] (2007).

    Article  ADS  MATH  Google Scholar 

  9. A. De Felice and S. Tsujikawa, “Solar system constraints on f(G) gravity models,” Phys. Rev. D, 80, 063516 (2009); arXiv:0907.1830v1 [hep-th] (2009).

    Article  ADS  Google Scholar 

  10. S. Nojiri and S. D. Odintsov, “Introduction to modified gravity and gravitational alternative for dark energy,” eConf, C0602061, 06 (2006); Internat. J. Geom. Meth. Mod. Phys., 4, 115–145 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  11. S. Nojiri and S. D. Odintsov, “Unified cosmic history in modified gravity: From F(R) theory to Lorentz noninvariant models,” Phys. Rep., 505, 59–144 (2011); arXiv:1011.0544v4 [gr-qc] (2010).

    Article  ADS  MathSciNet  Google Scholar 

  12. V. Fayaz, H. Hossienkhani, and A. Aghamohammadi, “Power-law solution for anisotropic universe in f(G) gravity,” Astrophys. Space Sci., 357, 136 (2015).

    Article  ADS  Google Scholar 

  13. N. M. Garcia, T. Harko, F. S. N. Lobo, and J. P. Mimoso, “Energy conditions in modified Gauss–Bonnet gravity,” Phys. Rev. D, 83, 104032 (2011); arXiv:1011.4159v2 [gr-qc] (2010).

    Article  ADS  Google Scholar 

  14. M. F. Shamir, “Anisotropic cosmological models in f(G) gravity,” Astrophys. Space Sci., 361, 147 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  15. M. F. Shamir, “Dynamics of anisotropic universe in f(G) gravity,” Astrophys. Space Sci., 362, 67 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  16. M. Sharif and H. I. Fatima, “Noether symmetries in f(G) gravity,” JETP, 122, 104–112 (2016).

    Article  ADS  Google Scholar 

  17. S. Nojiri, S. D. Odintsov, and M. Sami, “Dark energy cosmology from higher-order, string-inspired gravity, and its reconstruction,” Phys. Rev. D, 74, 046004 (2006); arXiv:hep-th/0605039v3 (2006)

    Article  ADS  Google Scholar 

  18. S. Nojiri and S. D. Odintsov, “Modified gravity and its reconstruction from the universe expansion history,” J. Phys.: Conf. Ser., 66, 012005 (2007).

    Google Scholar 

  19. A. De Felice, T. Suyama, and T. Tanaka, “Stability of Schwarzschild-like solutions in f(R, G) gravity models,” Phys. Rev. D, 83, 104035 (2011); arXiv:1102.1521v1 [gr-qc] (2011).

    Article  ADS  Google Scholar 

  20. S. Capozziello, A. N. Makarenko, and S. D. Odintsov, “Gauss–Bonnet dark energy by Lagrange multipliers,” Phys. Rev. D, 87, 084037 (2013); arXiv:1302.0093v2 [gr-qc] (2013).

    Article  ADS  Google Scholar 

  21. S. Capozziello, M. De Laurentis, and S. D. Odintsov, “Noether symmetry approach in Gauss–Bonnet cosmology,” Modern Phys. Lett. A, 29, 1450164 (2014).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  22. M. F. Shamir and F. Kanwal, “Noether symmetry analysis of anisotropic universe in modified gravity,” Eur. Phys. J. C, 77, 286 (2017); arXiv:1704.06653v1 [gr-qc] (2017).

    Article  ADS  Google Scholar 

  23. B. Wu and B. Ma, “Spherically symmetric solution of f(R, G) gravity at low energy,” Phys. Rev. D, 92, 044012 (2015); arXiv:1510.08552v1 [gr-qc] (2015).

    Article  ADS  MathSciNet  Google Scholar 

  24. K. Atazadeh and F. Darabi, “Energy conditions in f(R,G) gravity,” Gen. Rel. Grav., 46, 1664 (2014); arXiv: 1302.0466v4 [gr-qc] (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  25. L. Sebastiani, “Finite-time singularities in modified F(R,G)-gravity and singularity avoidance,” in: Cosmology, Quantum Vacuum, and Zeta Functions (Springer Proc. Phys., Vol. 137, D. Odintsov, D. Sáez-Gómez, and S. Xambó-Descamps, eds.), Springer, Berlin (2011), pp. 261–270; arXiv:1008.3041v2 [gr-qc] (2010).

    Google Scholar 

  26. M. Sharif and A. Ikram, “Energy conditions in f(G, T) gravity,” Eur. Phys. J. C, 76, 640 (2016); arXiv:1608.01182v3 [gr-qc] (2016).

    Article  ADS  Google Scholar 

  27. M. Sharif and A. Ikram, “Stability analysis of some reconstructed cosmological models in f(G, T) gravity,” Phys. Dark Univ., 17, 1–9 (2017); arXiv:1612.02037v2 [gr-qc] (2016).

    Article  Google Scholar 

  28. M. Sharif and A. Ikram, “Stability analysis of Einstein universe in f(G, T) gravity,” Internat. J. Modern Phys. D, 26, 1750084 (2017); arXiv:1704.05759v1 [gr-qc] (2017).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. M. Sharif and A. Ikram, “Energy conditions in f(G, T) gravity,” Eur. Phys. J. C, 76, 640 (2016); arXiv: 1608.01182v3 [gr-qc] (2016).

    Article  ADS  Google Scholar 

  30. M. F. Shamir and M. Ahmad, “Noether symmetry approach in f(G, T) gravity,” Eur. Phys. J. C, 77, 55 (2017); arXiv:1611.07338v2 [physics.gen-ph] (2016).

    Article  ADS  Google Scholar 

  31. M. F. Shamir and M. Ahmad, “Some exact solutions in f(G, T) gravity via Noether symmetries,” Modern Phys. Lett. A, 32, 1750086.

  32. M. F. Shamir, “Anisotropic universe in f(G, T) gravity,” Adv. High Energy Phys., 2017, 6378904 (2017).

    Article  MathSciNet  MATH  Google Scholar 

  33. M. Sharif and A. Ikram, “Thermodynamics in f(G, T) gravity,” Adv. High Energy Phys., 2018, 2563871 (2018).

    MATH  MathSciNet  Google Scholar 

  34. Z. Bhatti, M. Sharif, Z. Yousaf, and M. Ilyas, “Role of f(G, T) gravity on the evolution of relativistic stars,” Internat. J. Modern Phys. D, 27, 1850044 (2018).

    Article  ADS  MathSciNet  Google Scholar 

  35. M. Sharif and M. F. Shamir, “Plane symmetric solutions in f(R) gravity,” Modern Phys. Lett. A, 25, 1281–1288 (2010); arXiv:0912.1393v1 [gr-qc] (2009).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  36. M. F. Shamir, “Plane symmetric solutions in f(R, T) gravity,” Commun. Theor. Phys., 65, 301–307 (2016).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. R. Kantowski and R. K. Sachs, “Some spatially homogeneous anisotropic relativistic cosmological models,” J. Math. Phys., 7, 443–446 (1966).

    Article  ADS  MathSciNet  Google Scholar 

  38. W. Xing-Xiang, “Bianchi type-III string cosmological model with bulk viscosity in general relativity,” Chinese Phys. Lett., 22, 29–32 (2005).

    Article  ADS  Google Scholar 

  39. K. S. Thorne, “Primordial element formation, primordial magnetic fields, and the isotropy of the universe,” Astrophys. J., 148, 51–67 (1967).

    Article  ADS  Google Scholar 

  40. C. B. Collins and S. W. Hawking, “Why is the universe isotropic?” Astrophys. J., 180, 317–334 (1973).

    Article  ADS  MathSciNet  Google Scholar 

  41. S. R. Roy and S. K. Banerjee, “Bianchi type II string cosmological models in general relativity,” Class. Q. Grav., 12, 1943–1948 (1995).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  42. R. Bali and P. Kumawat, “Bulk viscous L.R.S. Bianchi type V tilted stiff fluid cosmological model in general relativity,” Phys. Lett. B, 665, 332–337 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. M. Sharif and M. Zubair, “Dynamics of Bianchi I universe with magnetized anisotropic dark energy,” Astrophys. Space Sci., 330, 399–405 (2010).

    Article  ADS  MATH  Google Scholar 

  44. G. Cognola, M. Gastaldi, and S. Zerbini, “On the stability of a class of modified gravitational models,” Internat. J. Theor. Phys., 47, 898–910 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  45. A. De Felice and S. Tsujikawa, “Construction of cosmologically viable f(G) gravity models,” Phys. Lett. B, 675, 1–8 (2009); arXiv:0810.5712v2 [hep-th] (2008).

    Article  ADS  Google Scholar 

  46. S. Tsujikawa, “Modified gravity models of dark energy,” in: Lectures on Cosmology (Lect. Notes Phys., Vol. 800, G. Wolschin, ed.), Springer, Berlin (2010), pp. 99–145; arXiv:1101.0191v1 [gr-qc] (2011).

    Google Scholar 

  47. S. Nojiri, S. D. Odintsov, and S. Tsujikawa, “Properties of singularities in the (phantom) dark energy universe,” Phys. Rev. D, 71, 063004 (2005); arXiv:hep-th/0501025v2 (2005).

    Article  ADS  Google Scholar 

  48. H. Takeno, “On plane wave solutions of field equations in general relativity,” Tensor, n.s., 7, 97–102 (1957).

    MathSciNet  MATH  Google Scholar 

  49. A. Peres, “Null electromagnetic fields in general relativity theory,” Phys. Rev., 118, 1105–1110 (1960).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. T. Nordtvedt and H. Pegels, “Electromagnetic plane wave solutions in general relativity,” Ann. Phys., 17, 426–435 (1962).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. V. Gaikwad and T. M. Karade, “Plane symmetric higher-dimensional space–times,” Acta Phys. Hungar., 67, 259–262 (1990).

    MathSciNet  Google Scholar 

  52. K. S. Adhav and T. M. Karade, Post Raag Reports, No. 279 (1994).

    Google Scholar 

  53. S. R. Bhoyar and A. G. Deshmukh, “Plane wave solutions of the field equations of general relativity–II,” Romanian Rep. Phys., 64, 933–944 (2012).

    Google Scholar 

  54. M. L. Bedran, M. O. Calvo, F. M. Paiva, and D. Soares, “Taub’s plane-symmetric vacuum spacetime reexamined,” Phys. Rev. D, 55, 3431–3439 (1997); arXiv:gr-qc/9608058v1 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  55. T. Feroze, A. Qadir, and M. Ziad, “Modified gravity with negative and positive powers of curvature: Unification of inflation and cosmic acceleration,” Phys. Rev. D, 68, 123512 (2003).

    Article  Google Scholar 

  56. M. F. Shamir and A. Saeed, “Plane symmetric solutions in f(\(\mathcal{G}\)) gravity,” JETP, 125, 1065–1070 (2017).

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. National University of Computer and Emerging Sciences, Lahore, Pakistan

    M. F. Shamir & A. Saeed

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  1. M. F. Shamir
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  2. A. Saeed
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Correspondence to M. F. Shamir.

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Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 197, No. 3, pp. 518–529, December, 2018.

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Shamir, M.F., Saeed, A. Plane Symmetric Solutions in f(\(\mathcal{G}\), T) Gravity. Theor Math Phys 197, 1845–1855 (2018). https://doi.org/10.1134/S0040577918120139

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