Skip to main content
SpringerLink
Log in

Constraints on a spherically symmetric 5-d braneworld

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

We study the effect of the extrinsic curvature within the context of braneworld with constant curvature and the restrictions on a spherically symmetric geometry embedded in a 5-d bulk. As a counterexample, we recover the Schwarzschild-de Sitter black hole but with umbilical points. In a second case we find the correct geometrical structure of a black hole but the Newtonian gravity cannot be restored implying that a higher dynamical embedding must be considered.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Arkani-Hamed, N., et al.: The hierarchy problem and new dimensions at a millimeter. Phys. Lett. B 429, 263 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  2. Arkani-Hamed, N., et al.: Infinitely large new dimensions. Phys. Lett. 84, 586 (2000)

    Article  MathSciNet  Google Scholar 

  3. Randall, L., Sundrum, R.: Large mass hierarchy from a small extra dimension. Phys. Rev. Lett. 83, 3370 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Randall, L., Sundrum, R.: An alternative to compactification. Phys. Rev. Lett. 83, 4690 (1999)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Dvali, G., Gabadadze, G., Porrati, M.: 4-D gravity on a brane in 5-D Minkowski space. Phys. Lett. B 485, 208 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. Sahni, V., Shtanov, Y.: New vistas in braneworld cosmology. IJMPD 11, 1515 (2002)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Sahni, V., Shtanov, Y.: Braneworld models of dark energy. JCAP 0311, 014 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  8. Shiromizu, T., Maeda, K., Sasaki, M.: The Einstein equations on the 3-brane world. Phys. Rev. D 62, 024012 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  9. Dick, R.: Brane worlds. Class. Quantum Gravity 18, R1 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Hogan, C.J.: Classical gravitational-wave backgrounds from formation of the brane world. Class. Quantum Gravity 18, 4039 (2001)

    Article  ADS  MATH  Google Scholar 

  11. Deffayet, C., Dvali, G., Gabadadze, G.: Accelerated universe from gravity leaking to extra dimensions. Phys. Rev. D 65, 044023 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  12. Alcaniz, J.S.: Some observational consequences of brane world cosmologies. Phys. Rev. D 65, 123514 (2002)

    Article  ADS  Google Scholar 

  13. Jain, D., Dev, A., Alcaniz, J.S.: Brane world cosmologies and statistical properties of gravitational lenses. Phys. Rev. D 66, 083511 (2002)

    Article  ADS  Google Scholar 

  14. Lue, A.: The phenomenology of Dvali–Gabadadze–Porrati cosmologies. Phys. Rep. 423, 1 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  15. Heydari-Fard, M., Shirazi, M., Jalalzadeh, S., Sepangi, H.R.: Accelerating universe in brane gravity with a confining potential. Phys. Lett. B 640, 1 (2006)

    Article  ADS  Google Scholar 

  16. Maia, M.D.: Covariant Analysis of Experimental Constraints on the Brane-World, Arxiv:astro-ph/0404370v1

  17. Maia, M.D., et al.: On the geometry of dark energy. Class. Quantum Gravity 22, 1623 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Maia, M.D., Silva, N., Fernandes, M.C.B.: Brane-world quantum gravity. JHEP 047, 0704 (2007)

    Google Scholar 

  19. Schlaefli, L.: Nota alla memoria del. Sig. Beltrami, Sugli spazzi di curvatura constante. Ann. di mat., 2 serie, 5, 170–193 (1871–1873)

  20. Riemann, B.: On the Hypothesis That Lie at the Foundations of Geometry (1854), translated by W. K. Clifford. Nature 8, 114 (1873)

  21. Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman Co., New York (1970)

    Google Scholar 

  22. Ade, P.A.R. et al.: (Planck Collaboration), Planck 2013 results. I. Overview of products and scientific results, Arxiv:astro-ph.CO/1303.5062

  23. Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Nash, J.: The imbedding problem for Riemannian manifolds. Ann. Math. 63, 20 (1956)

    Article  MathSciNet  MATH  Google Scholar 

  25. Greene, R.: Isometric embeddings of Riemannian and pseudo-Riemannian manifolds. Mem. Am. Math. Soc. 97, 1–63 (1970)

    Google Scholar 

  26. Primack, J.R.: Dark Matter and Structure Formation in the Universe, Arxiv:astro-ph/9707285

  27. Diemand, J., Moore, B.: The structure and evolution of cold dark matter halos. Adv. Sci. Lett. 4(2), 297 (2011)

    Article  Google Scholar 

  28. Peter, A.H.G.: Dark Matter, Arxiv:astro-ph.CO/1201.3942v1

  29. Isham, C.J., Salam, A., Strathdee, J.: F-dominance of gravity. Phys. Rev. 3, 4 (1971)

    Google Scholar 

  30. Maia, M.D., et al.: The deformable universes. Gen. Relativ. Gravit. 10, 2685 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  31. Maia, M.D., Monte, E.M.: On the stability of black-holes at the LHC. J. Phys. Conf. Ser. 314, 012124 (2011)

    Article  ADS  Google Scholar 

  32. Kasner, E.: The impossibility of Einstein fields inmersed in flat space of five dimensions. Am. J. Math. 43, 126 (1921)

    Article  MathSciNet  MATH  Google Scholar 

  33. Kasner, E.: Finite representation of the solar gravitational field in flat space of six dimensions. Am. J. Math. 43, 130 (1921)

    Article  MathSciNet  MATH  Google Scholar 

  34. Fronsdal, C.: Completion and embedding of the Schwarzschild solution. Phys. Rev. 116, 778 (1959)

    Article  MathSciNet  ADS  Google Scholar 

  35. Kruskal, M.D.: Maximal extension of Schwarzschild metric. Phys. Rev. 119, 1743 (1960)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. Szekeres, G.: On the singularities of a Riemannian manifold. Publ. Math. Debrecen 7, 285 (1960)

    MathSciNet  MATH  Google Scholar 

  37. Monte, E.M.: The embedding of Schwarzschild in braneworld. Int. J. Theor. Phys. 48, 409 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  38. Davidson, A., Paz, U.: Extensible embeddings of black-hole geometries. Found. Phys. 30, 5 (2000)

    Article  MathSciNet  Google Scholar 

  39. Eisenhart, L.P.: Riemannian Geometry. Princeton U. P. Sixth print, p. 159 ff (1966)

  40. Bergmann, P.G.: The Riddle of Gravitation. Dover Publications, New York (1992)

    Google Scholar 

Download references

Acknowledgments

I would like to thank Dr. John Fredsted for his valuable help in computer programming issues.

Author information

Authors and Affiliations

  1. Federal University of Latin-American Integration, Parque tecnológico de Itaipu, P.o.b: 2123, Foz do iguaçu, PR, 85867-670, Brazil

    A. J. S. Capistrano

Authors
  1. A. J. S. Capistrano
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. J. S. Capistrano.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Capistrano, A.J.S. Constraints on a spherically symmetric 5-d braneworld. Gen Relativ Gravit 45, 2647–2660 (2013). https://doi.org/10.1007/s10714-013-1608-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10714-013-1608-8

Keywords

Search

Navigation