Skip to main content
SpringerLink
Log in

Black holes in the brane world: Some exact solutions

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We briefly review methods for and results from constructing multidimensional solutions with an event horizon generated by matter localized on a brane. We investigate a particular exact solution of the black star type with the Schwarzschild-Tangherlini geometry in the bulk. We study the extrinsic curvature tensor, which predicts the matter distribution on the brane in accordance with the Israel conditions. We calculate all components of the four-dimensional Riemann tensor describing the intrinsic geometry on the brane surface and also investigate their asymptotic forms at a large distance from the center, limits on the horizon, and the asymptotic forms in the singularity neighborhood of a five-dimensional black hole in the case where the brane intersects it.

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. N. Arkani-Hamed, S. Dimopoulos, and G. R. Dvali, Phys. Lett. B, 429, 263–272 (1998); arXiv:hep-ph/9803315v1 (1998); I. Antoniadis, N. Arkani-Hamed, S. Dimopoulos, and G. Dvali, Phys. Lett. B, 436, 257–263 (1998); arXiv:hep-ph/9804398v1 (1998).

    Article  ADS  Google Scholar 

  2. V. A. Rubakov and M. E. Shaposhnikov, Phys. Lett. B, 125, 139–143 (1983); V. A. Rubakov, Phys. Usp., 44, 871–893 (2001); 46, 211–218 (2003).

    Article  ADS  Google Scholar 

  3. K. Akama, “Pregeometry,” in: Gauge Theory and Gravitation (Lect. Notes Phys., Vol. 176, K. Kikkawa, N. Nakanishi, and H. Nariai, eds.), Springer, Berlin (1983), pp. 267–271.

    Chapter  Google Scholar 

  4. T. Banks and W. Fischler, “A model for high energy scattering in quantum gravity,” arXiv:hep-th/9906038v1 (1999); I. Ya. Aref’eva, Phys. Part. Nucl., 31, No. 7a, 169–180 (2000); arXiv:hep-th/9910269v1; 41, 1562–1578 (2010); arXiv:0912.5481v1 [hep-th] (2009); S. Dimopoulos and G. Landsberg, Phys. Rev. Lett., 87, 161602 (2001); arXiv:hep-ph/0106295v1 (2001); S. B. Giddings and S. Thomas, Phys. Rev. D, 65, 056010 (2002); arXiv:hep-ph/0106219v4 (2001).

    Google Scholar 

  5. R. Emparan and H. S. Reall, Living Rev. Relativ., 11, 2008–6 (2008).

    Google Scholar 

  6. R. Gregory, “Braneworld black holes,” in: Physics of Black Holes: A Guided Tour (Lect. Notes Phys., Vol. 769, E. Papantonopoulos, ed.), Springer, Berlin (2009), pp. 259–298; arXiv:0804.2595v1 [hep-th] (2008).

    Chapter  Google Scholar 

  7. P. Kanti, J. Phys. (Conf. Ser.), 189, 012020 (2009); arXiv:0903.2147v1 [hep-th] (2009).

    Article  Google Scholar 

  8. W. Israel, Il Nuovo Cimento B, 44, 1–14 (1966); Erratum, 48, 463–463 (1967); Nuovo Cimento Suppl., 44, 4349 (1966); C. Lanczos, Phys. Z., 23, 539–543 (1922).

    Article  ADS  Google Scholar 

  9. T. Shiromizu, K. Maeda, and M. Sasaki, Phys. Rev. D, 62, 024012 (2000); arXiv:gr-qc/9910076v3 (1999).

    Article  ADS  MathSciNet  Google Scholar 

  10. N. Dadhich, R. Maartens, P. Papadopoulos, and V. Rezania, Phys. Lett. B, 487, 1–6 (2000); arXiv:hep-th/0003061v3 (2000); C. Germani and R. Maartens, Phys. Rev. D, 64, 124010 (2001); arXiv:hep-th/0107011v3 (2001); R. Casadio, A. Fabbri, and L. Mazzacurati, Phys. Rev. D, 65, 084040 (2002); arXiv:gr-qc/0111072v2 (2001); K. A. Bronnikov, V. N. Melnikov, and H. Dehnen, Phys. Rev. D, 68, 024025 (2003); arXiv:gr-qc/0304068v1 (2003).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. R. M. Wald, General Relativity, Univ. Chicago Press, Chicago (1984).

    MATH  Google Scholar 

  12. G. G. Kuzmin, Astron. Rep., 33, No. 1, 27–45 (1956).

    Google Scholar 

  13. F. R. Tangherlini, Nuovo Cimento, 27, 636–651 (1963).

    Article  MATH  MathSciNet  Google Scholar 

  14. S. Creek, R. Gregory, P. Kanti, and B. Mistry, Class. Q. Grav., 23, 6633–6657 (2006); arXiv:hep-th/0606006v1 (2006).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  15. D. M. Gingrich, Phys. Rev. D, 81, 057702 (2010); arXiv:1001.0626v3 [hep-ph] (2010); J. Phys. G, 37, 105008 (2010); arXiv:0912.0826v4 [hep-ph] (2009).

    Article  ADS  Google Scholar 

  16. A. A. Andrianov and M. A. Kurkov, Phys. Rev. D, 82, 104027 (2010); arXiv:1008.2705v3 [hep-th] (2010).

    Article  ADS  Google Scholar 

  17. H. Bateman and A. Erdélyi, Higher Transcendental Functions, Vol. 3, Elliptic and Modular Functions, Lamé and Mathieu Functions, McGraw-Hill, New York (1955).

    Google Scholar 

  18. P. Binétruy, C. Deffayet, and D. Langlois, Nucl. Phys. B, 565, 269–287 (2000); arXiv:hep-th/9905012v2 (1999).

    Article  MATH  ADS  Google Scholar 

  19. N. A. Obers, “Black holes in higher-dimensional gravity,” in: Physics of Black Holes: A Guided Tour (Lect. Notes Phys., Vol. 769, E. Papantonopoulos, ed.), Springer, Berlin (2009), pp. 211–258; arXiv:0802.0519v1 [hep-th] (2008).

    Chapter  Google Scholar 

  20. L. Randall and R. Sundrum, Phys. Rev. Lett., 83, 3370–3373 (1999); arXiv:hep-ph/9905221v1 (1999); 83, 4690–4693 (1999); C. Galfard, C. Germani, A. Ishibashi, Phys. Rev. D, 73, 064014 (2006); arXiv:hep-th/0512001v3 (2005).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  21. R. Emparan and H. S. Reall, Phys. Rev. D, 65, 084025 (2002); arXiv:hep-th/0110258v2 (2001).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Saint Petersburg State University, St. Petersburg, Russia

    A. A. Andrianov & M. A. Kurkov

Authors
  1. A. A. Andrianov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. A. Kurkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. A. Andrianov.

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 169, No. 2, pp. 307–322, November, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Andrianov, A.A., Kurkov, M.A. Black holes in the brane world: Some exact solutions. Theor Math Phys 169, 1629–1642 (2011). https://doi.org/10.1007/s11232-011-0140-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-011-0140-9

Keywords

Search

Navigation