Advertisement

Gravitation and Cosmology

, Volume 24, Issue 1, pp 71–79 | Cite as

Stability of a d-Dimensional Thin-Shell Wormhole Surrounded by Quintessence

  • Ayan BanerjeeEmail author
  • Kimet Jusufi
  • Sebastian Bahamonde
Article

Abstract

We study the stability of different higher dimensional thin–shell wormholes (HDTSW) in general relativity with a cosmological constant. We show that a d-dimensional thin–shell wormhole surrounded by quintessence can have three different throat geometries: spherical, planar and hyperbolic. Unlike the spherical geometry, the planar and hyperbolic geometries allow different topologies that can be interpreted as higher-dimensional domain walls or branes connecting two universes. To construct these geometries, we use the cut-and-paste procedure by joining two identical vacuum space-time solutions. Properties such as the null energy condition and geodesics are also studied. A linear stability analysis around the static solutions is carried out, taking into account a more general HDTSW geometry than previous works, so it is possible to recover other well-known stability HDTSW conditions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Flamm, Phys. Z. 17, 448 (1916).Google Scholar
  2. 2.
    A. Einstein and N. Rosen, Phys. Rev. 48, 73–77 (1935).ADSCrossRefGoogle Scholar
  3. 3.
    R.W. Fuller and J. A. Wheeler, Phys. Rev. 128, 919–929 (1962).ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    M. S. Morris and K. S. Thorne, Am. J. Phys. 56, 395 (1988).ADSCrossRefGoogle Scholar
  5. 5.
    M. Visser, Lorentzian Wormholes (AIP Press, New York, 1996).Google Scholar
  6. 6.
    M. Morris, K. S. Thorne and U. Yurtsever, Phys.Rev. Lett. 61, 1446 (1988).ADSCrossRefGoogle Scholar
  7. 7.
    J. P. S. Lemos, F. S. N. Lobo, and S. Quinet de Oliveira, Phys. Rev. D 68, 064004 (2003).ADSCrossRefGoogle Scholar
  8. 8.
    M. Visser, Nuclear Physics B 328, 203 (1989).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Visser, Phys. Rev. D 39, 3182 (1989).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    W. Israel, Nuovo Cimento B 44, 1 (1966).ADSCrossRefGoogle Scholar
  11. 11.
    A. Papapetrou and A. Hamoui, Ann. Inst. Henri Poincare 9, 179 (1968).ADSGoogle Scholar
  12. 12.
    N. Sen, Ann. Phys. (Leipzig) 73, 365 (1924).ADSCrossRefGoogle Scholar
  13. 13.
    K. Lanczos, ibid. 74, 518 (1924).ADSGoogle Scholar
  14. 14.
    P. Musgrave and K. Lake, Class. Quantum Grav. 13, 1885 (1996).ADSCrossRefGoogle Scholar
  15. 15.
    E. Poisson and M. Visser, Phys. Rev. D 52, 7318 (1995).ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    K. A. Bronnikov, R. A. Konoplya, and A. Zhidenko, Phys. Rev. D 86, 024028 (2012).ADSCrossRefGoogle Scholar
  17. 17.
    E. F. Eiroa and G. E. Romero, Gen. Relativ. Gravit. 36, 651 (2004).ADSCrossRefGoogle Scholar
  18. 18.
    F. S. N. Lobo and P. Crawford, Class. Quantum Grav. 21, 391 (2004).ADSCrossRefGoogle Scholar
  19. 19.
    M. Thibeault, C. Simeone, and E. F. Eiroa, Gen. Relativ. Gravit. 38, 1593 (2006).ADSCrossRefGoogle Scholar
  20. 20.
    E. F. Eiroa and C. Simeone, Phys. Rev. D 71, 127501 (2005).ADSCrossRefGoogle Scholar
  21. 21.
    M. G. Richarte and C. Simeone, Int. J.Mod. Phys. D 17, 1179 (2008).ADSCrossRefGoogle Scholar
  22. 22.
    G. Dotti, J. Oliva, and R. Troncoso, Phys. Rev. D 75, 024002 (2007).ADSCrossRefGoogle Scholar
  23. 23.
    A. A.Usmani, F. Rahaman, Saibal Ray, Sk. A. Rakib, Z. Hasan, and Peter K. F. Kuhfittig, arXiv: 1001.1415.Google Scholar
  24. 24.
    F. Rahaman, K. A. Rahman, Sk. A. Rakib, and Peter K. F. Kuhfittig, Gen. Rel. Grav. 42, 2901–2912 (2010).ADSCrossRefGoogle Scholar
  25. 25.
    M. G. Richarte and C. Simeone, Phys. Rev. D 80, 104033 (2009); Erratum 81, 109903 (2010).ADSCrossRefGoogle Scholar
  26. 26.
    J. P. S. Lemos and F. S. N. Lobo, Phys. Rev. D 69, 104007 (2004).ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    J. P. S. Lemos and F. S. N. Lobo, Phys. Rev. D 78, 044030 (2008).ADSMathSciNetCrossRefGoogle Scholar
  28. 28.
    M. Sharif and M. Azam, JCAP 1304, 023 (2013).ADSCrossRefGoogle Scholar
  29. 29.
    S. Habib Mazharimousavi, M. Halilsoy, and Z. Amirabi, Phys. Rev. D 89, 084003 (2014).ADSCrossRefGoogle Scholar
  30. 30.
    M. R. Setare and A. Sepehri, JHEP 1503, 079 (2015).ADSCrossRefGoogle Scholar
  31. 31.
    Mubasher Jamil, Peter K. F. Kuhfittig, Farook Rahaman, and Sk. A. Rakib, Eur. Phys. J. C 67, 513 (2010).ADSCrossRefGoogle Scholar
  32. 32.
    Cecilia Bejarano and Ernesto F. Eiroa, Phys. Rev. D 84, 064043 (2011).ADSCrossRefGoogle Scholar
  33. 33.
    Ernesto F. Eiroa, Phys. Rev. D 80, 044033 (2009).ADSCrossRefGoogle Scholar
  34. 34.
    F. S. N. Lobo, Phys. Rev. D 71, 084011 (2005).ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    S. Sushkov, Phys. Rev. D 71, 043520 (2005).ADSCrossRefGoogle Scholar
  36. 36.
    T. Multamaki, M. Manera, and E. Gaztanaga, Phys. Rev. D 69, 023004 (2004).ADSCrossRefGoogle Scholar
  37. 37.
    Peter K. F. Kuhfittig, Acta Phys. Polon. B 41, 2017–2019 (2010).Google Scholar
  38. 38.
    N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys Lett. B 429, 263 (1998).ADSCrossRefGoogle Scholar
  39. 39.
    I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys Lett. B 436, 257 (1998).ADSCrossRefGoogle Scholar
  40. 40.
    L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 3370 (1999).ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    L. Randall and R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999).ADSMathSciNetCrossRefGoogle Scholar
  42. 42.
    R. C. Myers and M. J. Perry, Ann. Phys. 172, 304 (1986).ADSCrossRefGoogle Scholar
  43. 43.
    V.N. Melnikov, in Proc. 8thMarcel GrossmanMeeting (Jerusalem, Israel, 1997).Google Scholar
  44. 44.
    U. Kasper, M. Rainer, and A. Zhuk, Gen. Rel. Grav. 29, 1123 (1997).ADSCrossRefGoogle Scholar
  45. 45.
    K. A. Bronnikov and V. N. Melnikov, Grav. Cosmol. 1, 155 (1995).ADSGoogle Scholar
  46. 46.
    S. E. P. Bergliaffa, Mod. Phys. Let. A 15, 531 (2000).ADSCrossRefGoogle Scholar
  47. 47.
    H. Kim, S. Moon, and J. H. Yee, JHEP 0202, 046 (2002).ADSCrossRefGoogle Scholar
  48. 48.
    J. Ponce de Leon and N. Cruz, Gen. Rel. Grav. 32, 1207 (2000).ADSCrossRefGoogle Scholar
  49. 49.
    P. Gonzales-Diaz, Phys. Lett. B 247, 251 (1990).ADSCrossRefGoogle Scholar
  50. 50.
    X. Jianjun and J. Sicong, Mod. Phys. Lett. 6, 251 (1990).Google Scholar
  51. 51.
    M. Cataldo, P. Salgado, and P. Minning, Phys. Rev. D 66, 124008 (2002).ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Mauricio Cataldo, Fernanda Aróstica, and Sebastian Bahamonde, Eur. Phys. J. C 73, 2517 (2013).ADSCrossRefGoogle Scholar
  53. 53.
    S. Kar and D. Sahdev, Phys. Rev. D 53, 722 (1996).ADSMathSciNetCrossRefGoogle Scholar
  54. 54.
    M. K. Zangeneh, F. S. N. Lobo, and N. Riazi, arXiv: 1406.5703.Google Scholar
  55. 55.
    A. DeBenedictis and D. Das, Nucl. Phys. B 653, 279–304 (2003).ADSCrossRefGoogle Scholar
  56. 56.
    M. H. Dehghani and S. H. Hendi, Gen. Rel. Grav. 41, 1853 (2009).ADSCrossRefGoogle Scholar
  57. 57.
    B. Bhawal and S. Kar, Phys. Rev. D 46, 2464 (1992).ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    G. A. S. Dias and J. P. S. Lemos, Phys. Rev. D 82, 084023 (2010).ADSCrossRefGoogle Scholar
  59. 59.
    F. Rahaman, M. Kalam, and S. Chakraborty, Gen. Rel. Grav. 38, 1687-1695 (2006).ADSCrossRefGoogle Scholar
  60. 60.
    S. H. Mazharimousavi, M. Halilsoy, and Z. Amirabi, Phys. Lett. A 375, 231 (2011).ADSMathSciNetCrossRefGoogle Scholar
  61. 61.
    S. H. Mazharimousavi, M. Halilsoy, and Z. Amirabi, Class. Quantum Grav. 28, 025004 (2011).ADSCrossRefGoogle Scholar
  62. 62.
    Ernesto F. Eiroa and Claudio Simeone, Int. J. Mod. Phys. D 21, 1250033 (2012).ADSCrossRefGoogle Scholar
  63. 63.
    Goncalo A. S. Dias and JoséP. S. Lemos, Phys. Rev. D 82, 084023 (2010).ADSCrossRefGoogle Scholar
  64. 64.
    M. H. Dehghani and M. R. Mehdizadeh, Phys. Rev. D 85, 024024 (2012).ADSCrossRefGoogle Scholar
  65. 65.
    Songbai Chen, Bin Wang, and Rukeng Su, Phys. Rev. D 77, 124011, (2008).ADSMathSciNetCrossRefGoogle Scholar
  66. 66.
    V. V. Kiselev, Class. Quantum Grav. 20, 1187 (2003).ADSCrossRefGoogle Scholar
  67. 67.
    S. Fernando, Gen. Rel. Grav. 44, 1857 (2012).ADSCrossRefGoogle Scholar
  68. 68.
    Y. Zhang and Y. X. Gui, Class. Quantum Grav. 23, 6141 (2006).ADSCrossRefGoogle Scholar
  69. 69.
    A. Younas, S. Hussain, M. Jamil and S. Bahamonde, Phys. Rev. D 92, 084042 (2015).ADSMathSciNetCrossRefGoogle Scholar
  70. 70.
    M. Azreg-Ainou, S. Bahamonde, and M. Jamil, Eur. Phys. J. C 77, 414 (2017).ADSCrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  • Ayan Banerjee
    • 1
    Email author
  • Kimet Jusufi
    • 2
  • Sebastian Bahamonde
    • 3
  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia
  2. 2.Physics DepartmentState University of TetovoTetovoMacedonia
  3. 3.Department of MathematicsUniversity College LondonLondonUK

Personalised recommendations