Schwarzschild generalized black hole horizon and the embedding space

Regular Article - Theoretical Physics

Abstract

By performing a Taylor expansion along the extra dimension of a metric describing a black hole on a brane, we explore the influence of the embedding space on the black hole horizon. In particular, it is shown that the existence of a Kottler correction of the black hole on the brane, in a viable braneworld scenario, might represent the radius of the black string collapsing to zero, for some point(s) on the black string axis of symmetry along the extra dimension. Further scrutiny on such black hole corrections by braneworld effects is elicited, the well-known results in the literature are recovered as limiting cases, and we assert and show that when the radius of the black string transversal section is zero, as one moves away from the brane into the bulk, is indeed a singularity.

Keywords

Black Hole Cosmological Constant Extra Dimension Weyl Tensor Black Hole Horizon 

Notes

Acknowledgements

J.M. Hoff da Silva is grateful to CNPq grant 482043/2011-3, and R. da Rocha is grateful to Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) grants 476580/2010-2 and 304862/2009-6 for financial support.

References

  1. 1.
    N. Dadhich, R. Maartens, P. Papadopoulos, V. Rezania, Phys. Lett. B 487, 1 (2000). hep-th/0003061 MathSciNetADSMATHGoogle Scholar
  2. 2.
    R. Casadio, A. Fabbri, L. Mazzacurati, Phys. Rev. D 65, 084040 (2002). gr-qc/0111072 MathSciNetADSGoogle Scholar
  3. 3.
    M. Bruni, C. Germani, R. Maartens, Phys. Rev. Lett. 87, 231302 (2001). gr-qc/0108013 MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    T. Tanaka, Prog. Theor. Phys. Suppl. 148, 307 (2003). gr-qc/0203082 ADSCrossRefGoogle Scholar
  5. 5.
    R. Emparan, A. Fabbri, N. Kaloper, J. High Energy Phys. 0208, 043 (2002). hep-th/0206155 MathSciNetADSCrossRefGoogle Scholar
  6. 6.
    A. Chamblin, H.S. Reall, H.-a. Shinkai, T. Shiromizu, Phys. Rev. D 63, 064015 (2001). hep-th/0008177 MathSciNetADSGoogle Scholar
  7. 7.
    S.B. Giddings, E. Katz, L. Randall, J. High Energy Phys. 0003, 023 (2000). hep-th/0002091 MathSciNetADSCrossRefGoogle Scholar
  8. 8.
    L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 4690 (1999). hep-th/9906064 MathSciNetADSMATHCrossRefGoogle Scholar
  9. 9.
    L. Randall, R. Sundrum, Phys. Rev. Lett. 83, 3370–3373 (1999). hep-ph/9905221 MathSciNetADSMATHCrossRefGoogle Scholar
  10. 10.
    M. Gogberashvili, Europhys. Lett. 49, 396 (2000). hep-ph/9812365 ADSCrossRefGoogle Scholar
  11. 11.
    R. Casadio, L. Mazzacurati, Mod. Phys. Lett. A 18, 651 (2003). gr-qc/0205129 MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    T. Shiromizu, K. Maeda, M. Sasaki, Phys. Rev. D 62, 043523 (2000) MathSciNetGoogle Scholar
  13. 13.
    S.S. Seahra, C. Clarkson, R. Maartens, Phys. Rev. Lett. 94, 121302 (2005). gr-qc/0408032 ADSCrossRefGoogle Scholar
  14. 14.
    A.N. Aliev, A.E. Gumrukcuoglu, Class. Quantum Gravity 21, 5081 (2004). hep-th/0407095 MathSciNetADSMATHCrossRefGoogle Scholar
  15. 15.
    R. Maartens, K. Koyama, Living Rev. Relativ. 13, 5 (2010). arXiv:1004.3962 ADSGoogle Scholar
  16. 16.
    W. Israel, Nuovo Cimento B 44, 1 (1966) ADSCrossRefGoogle Scholar
  17. 17.
    R.M. Wald, General Relativity (Univ. of Chicago Press, Chicago, 1984) MATHGoogle Scholar
  18. 18.
    A. Chamblin, S.W. Hawking, H.S. Reall, Phys. Rev. D 61, 065007 (2000). hep-th/9909205 MathSciNetADSGoogle Scholar
  19. 19.
    R. Gregory, R. Laflamme, Phys. Rev. Lett. 70, 2837 (1993). hep-th/9301052 MathSciNetADSMATHCrossRefGoogle Scholar
  20. 20.
    F. Kottler, Ann. Phys. 56, 410 (1918) Google Scholar
  21. 21.
    J.C. Long, H.W. Chan, A.B. Churnside, E.A. Gulbis, M.C.M. Varney, J.C. Price, Nature 421, 922 (2003) ADSCrossRefGoogle Scholar
  22. 22.
    A. Das, A. DeBenedictis, Prog. Theor. Phys. 108, 119 (2002). gr-qc/0110083 MathSciNetADSMATHCrossRefGoogle Scholar
  23. 23.
    I.C. Jardim, R.R. Landim, G. Alencar, R.N.C. Filho, Phys. Rev. D 84, 064019 (2011). arXiv:1105.4578 [gr-qc] ADSGoogle Scholar
  24. 24.
    W.A. Hiscock, Phys. Rev. D 39, 1067 (1989) MathSciNetADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg and Società Italiana di Fisica 2012

Authors and Affiliations

  1. 1.Departamento de Física e QuímicaUniversidade Estadual PaulistaGuaratinguetáBrazil
  2. 2.Centro de Matemática, Computação e CogniçãoUniversidade Federal do ABC 09210-170Santo AndréBrazil

Personalised recommendations