Gravity of a noncanonical global monopole: conical topology and compactification

  • Ilham Prasetyo
  • Handhika S. RamadhanEmail author
Research Article


We obtain solutions of Einstein’s equations describing gravitational field outside a noncanonical global monopole with cosmological constant. In particular, we consider two models of k-monopoles: the Dirac–Born–Infeld and the power-law types, and study their corresponding exterior gravitational fields. For each model we found two types of solutions. The first of which are global k-monopole black hole with conical global topology. These are generalizations of the Barriola–Vilenkin solution of global monopole. The appearance of noncanonical kinetic terms does not modify the critical symmetry-breaking scale, \(\eta _{crit}\), but it does affect the corresponding horizon(s). The second type of solution is compactification, whose topology is a product of two 2-dimensional spaces with constant curvatures; \({\mathcal Y}_4\rightarrow {\mathcal Z}_2\times S^2\), with \({\mathcal Y}, {\mathcal Z}\) can be de Sitter, Minkowski, or Anti-de Sitter, and \(S^2\) is the 2-sphere. We investigate all possible compactifications and show that the nonlinearity of kinetic terms opens up new channels which are otherwise non-existent. For \(\Lambda =0\) four-dimensional geometry, we conjecture that these compactification channels are their (possible) non-static super-critical states, right before they undergo topological inflation.


Exact solutions Deficit angle Compactification Born-Infeld 



We thank Ardian Atmaja and Jose Blanco-Pillado for useful discussions and comments on the early manuscript. This work was partially supported by the Research-Cluster-Grant-Program of the University of Indonesia No. 1862/UN.R12/HKP.05.00/2015.


  1. 1.
    Kibble, T.W.B.: Topology of cosmic domains and strings. J. Phys. A 9, 1387 (1976)ADSCrossRefzbMATHGoogle Scholar
  2. 2.
    Vilenkin, A., Shellard, E.P.S.: Cosmic Strings and other Topological Defects. Cambridge University Press, Cambridge (1994)zbMATHGoogle Scholar
  3. 3.
    ’t Hooft, G.: Magnetic monopoles in unified gauge theories. Nucl. Phys. B 79, 276 (1974)ADSMathSciNetCrossRefGoogle Scholar
  4. 4.
    Polyakov, A.M.: Particle spectrum in the quantum field theory. JETP Lett. 20, 194 (1974) [Pisma Zh. Eksp. Teor. Fiz. 20, 430 (1974)]Google Scholar
  5. 5.
    Manton, N.S., Sutcliffe, P.: Topological solitons. Cambridge University Press, Cambridge (2004)CrossRefzbMATHGoogle Scholar
  6. 6.
    Barriola, M., Vilenkin, A.: Gravitational field of a global monopole. Phys. Rev. Lett. 63, 341 (1989)ADSCrossRefGoogle Scholar
  7. 7.
    Harari, D., Lousto, C.: Repulsive gravitational effects of global monopoles. Phys. Rev. D 42, 2626 (1990)ADSCrossRefGoogle Scholar
  8. 8.
    Olasagasti, I., Vilenkin, A.: Gravity of higher dimensional global defects. Phys. Rev. D 62, 044014 (2000). hep-th/0003300
  9. 9.
    Cho, I., Vilenkin, A.: Gravity of superheavy higher dimensional global defects. Phys. Rev. D 68, 025013 (2003). hep-th/0304219
  10. 10.
    Liebling, S.L.: Static gravitational global monopoles. Phys. Rev. D 61, 024030 (2000). gr-qc/9906014
  11. 11.
    Vilenkin, A.: Topological inflation. Phys. Rev. Lett. 72, 3137 (1994). hep-th/9402085
  12. 12.
    Linde, A.D.: Monopoles as big as a universe. Phys. Lett. B 327, 208 (1994). astro-ph/9402031
  13. 13.
    Cho, I., Vilenkin, A.: Space-time structure of an inflating global monopole. Phys. Rev. D 56, 7621 (1997). gr-qc/9708005
  14. 14.
    Babichev, E.: Global topological k-defects. Phys. Rev. D 74, 085004 (2006). hep-th/0608071
  15. 15.
    Babichev, E.: Gauge k-vortices. Phys. Rev. D 77, 065021 (2008). arXiv:0711.0376 [hep-th]
  16. 16.
    Armendariz-Picon, C., Damour, T., Mukhanov, V.F.: k-Inflation. Phys. Lett. B 458, 209 (1999). hep-th/9904075
  17. 17.
    Sarangi, S.: DBI global strings. JHEP 0807, 018 (2008). arXiv:0710.0421 [hep-th]
  18. 18.
    Babichev, E., Brax, P., Caprini, C., Martin, J., Steer, D.A.: Dirac Born Infeld (DBI) cosmic strings. JHEP 0903, 091 (2009). arXiv:0809.2013 [hep-th]
  19. 19.
    Pavlovsky, O.V.: Chiral Born–Infeld theory: topological spherically symmetrical solitons. Phys. Lett. B 538, 202 (2002). hep-ph/0204313
  20. 20.
    Ramadhan, H.S.: Higher-dimensional DBI solitons. Phys. Rev. D 85, 065014 (2012). arXiv:1201.1591 [hep-th]
  21. 21.
    Ramadhan, H.S.: On DBI textures with generalized Hopf fibration. Phys. Lett. B 713, 297 (2012). arXiv:1205.6282 [hep-th]
  22. 22.
    Born, M., Infeld, L.: Foundations of the new field theory. Proc. R. Soc. Lond. A 144, 425 (1934)ADSCrossRefGoogle Scholar
  23. 23.
    Li, X.Z., Liu, D.J.: Tachyon monopole. Int. J. Mod. Phys. A 20, 5491 (2005). gr-qc/0510116
  24. 24.
    Jin, X.H., Li, X.Z., Liu, D.J.: Gravitating global k-monopole. Class. Quantum Gravity 24, 2773 (2007). arXiv:0704.1685[gr-qc]
  25. 25.
    Liu, D.J., Zhang, Y.L., Li, X.Z.: A self-gravitating Dirac–Born–Infeld global monopole. Eur. Phys. J. C 60, 495 (2009). arXiv:0902.1051 [hep-th]
  26. 26.
    Li, X.Z., Hao, J.G.: Global monopole in asymptotically dS/AdS space-time. Phys. Rev. D 66, 107701 (2002). hep-th/0210050
  27. 27.
    Bertrand, B., Brihaye, Y., Hartmann, B.: de Sitter/anti-de Sitter global monopoles. Class. Quantum Gravity 20, 4495 (2003). hep-th/0304026
  28. 28.
    Tangherlini, F.R.: Schwarzschild field in n dimensions and the dimensionality of space problem. Nuovo Cim. 27, 636 (1963)MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Gregory, R.: Cosmic p-branes. Nucl. Phys. B 467, 159 (1996). hep-th/9510202
  30. 30.
    Marunovic, A., Murkovic, M.: A novel black hole mimicker: a boson star and a global monopole nonminimally coupled to gravity. Class. Quantum Gravity 31, 045010 (2014). arXiv:1308.6489[gr-qc]
  31. 31.
    Gregory, R.: Nonsingular global strings. Phys. Rev. D 54, 4955 (1996). gr-qc/9606002
  32. 32.
    Olasagasti, I.: Gravitating global defects: the gravitational field and compactification. Phys. Rev. D 63, 124016 (2001). hep-th/0101203
  33. 33.
    Blanco-Pillado, J.J., Reina, B., Sousa, K., Urrestilla, J.: Supermassive cosmic string compactifications. JCAP 1406, 001 (2014). arXiv:1312.5441 [hep-th]
  34. 34.
    Ortiz, M.E.: A new look at supermassive cosmic strings. Phys. Rev. D 43, 2521 (1991)ADSCrossRefGoogle Scholar
  35. 35.
    Nariai, H.: On some static solutions of Einstein’s gravitational field equations in a spherically symmetric case. Sci. Rep. Tohoku Univ. 34, 160 (1950)ADSMathSciNetGoogle Scholar
  36. 36.
    Bertotti, B.: Uniform electromagnetic field in the theory of general relativity. Phys. Rev. 116, 1331 (1959)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Robinson, I.: A solution of the Maxwell–Einstein equations. Bull. Acad. Pol. Sci. Ser. Sci. Math. Astron. Phys. 7, 351 (1959)zbMATHGoogle Scholar
  38. 38.
    Plebanński, J.F., Hacyan, S.: Some exceptional electrovac type D metrics with cosmological constant. J. Math. Phys. 20, 1004 (1979)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    Randjbar-Daemi, S., Salam, A., Strathdee, J.A.: Spontaneous compactification in six-dimensional Einstein–Maxwell theory. Nucl. Phys. B 214, 491 (1983)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Salam, A., Sezgin, E.: Chiral compactification on Minkowski \(\times S^2\) of \(N=2\) Einstein–Maxwell supergravity in six-dimensions. Phys. Lett. B 147, 47 (1984)ADSMathSciNetCrossRefGoogle Scholar
  41. 41.
    Blanco-Pillado, J.J., Salem, M.P.: Observable effects of anisotropic bubble nucleation. JCAP 1007, 007 (2010). arXiv:1003.0663 [hep-th]
  42. 42.
    Blanco-Pillado, J.J., Schwartz-Perlov, D., Vilenkin, A.: Quantum tunneling in flux compactifications. JCAP 0912, 006 (2009). arXiv:0904.3106 [hep-th]
  43. 43.
    Blanco-Pillado, J.J., Schwartz-Perlov, D., Vilenkin, A.: Transdimensional tunneling in the multiverse. JCAP 1005, 005 (2010). arXiv:0912.4082 [hep-th]

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Departemen Fisika, FMIPAUniversitas IndonesiaDepokIndonesia

Personalised recommendations