Table of Contents Author Guidelines Submit a Manuscript
Advances in High Energy Physics
Volume 2014, Article ID 926589, 7 pages
http://dx.doi.org/10.1155/2014/926589
Research Article

Cardy-Verlinde Formula and Its Self-Gravitational Corrections for Regular Black Holes

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan

Received 28 March 2014; Accepted 3 May 2014; Published 21 May 2014

Academic Editor: Ming Liu

Copyright © 2014 M. Sharif and Rabia Saleem. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3.

Linked References

  1. J. Michell, “On the means of discovering the distance, magnitude, &c. of the fixed stars, in consequence of the diminution of the velocity of their light, in case such a diminution should be found to take place in any of them, and such other data should be procured from observations, as would be farther necessary for that purpose,” Philosophical Transactions of the Royal Society, vol. 74, pp. 35–57, 1784. View at Publisher · View at Google Scholar
  2. J. A. Wheeler, “Our universe: the known and the unknown,” The American Scientist, vol. 56, p. 1, 1968. View at Google Scholar
  3. S. W. Hawking, “Black hole explosions?” Nature, vol. 248, no. 5443, pp. 30–31, 1974. View at Publisher · View at Google Scholar · View at Scopus
  4. J. B. Hartle and S. W. Hawking, “Path-integral derivation of black-hole radiance,” Physical Review D, vol. 13, no. 8, pp. 2188–2203, 1976. View at Publisher · View at Google Scholar · View at Scopus
  5. Q. Q. Jiang and X. Cai, “Remarks on self-interaction correction to black hole radiation,” Journal of High Energy Physics, vol. 2003, no. 11, article 110, 2009. View at Publisher · View at Google Scholar
  6. P. Kraus and F. Wilczek, “Self-interaction correction to black hole radiance,” Nuclear Physics B, vol. 433, no. 2, pp. 403–420, 1995. View at Google Scholar · View at Scopus
  7. P. Kraus and F. Wilczek, “Effect of self-interaction on charged black hole radiance,” Nuclear Physics B, vol. 437, no. 1, pp. 231–242, 1995. View at Google Scholar · View at Scopus
  8. P. Painleve, “La mécanique classique et la théorie de la relativité,” Comptes Rendus de l'Académie des Sciences, vol. 173, pp. 677–680, 1921. View at Google Scholar
  9. E. C. Vagenas, “Generalization of the KKW analysis for black hole radiation,” Physics Letters B, vol. 559, no. 1-2, pp. 65–73, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  10. M. K. Parikh and F. Wilczek, “Hawking radiation as tunneling,” Physical Review Letters, vol. 85, no. 24, pp. 5042–5045, 2000. View at Publisher · View at Google Scholar · View at MathSciNet
  11. S. Hemming and E. Keski-Vakkuri, “Hawking radiation from AdS black holes,” Physical Review D, vol. 64, no. 4, Article ID 044006, 8 pages, 2001. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Y. Kwon, “Hawking radiation in AdS2 black hole,” Il Nuovo Cimento della Società Italiana di Fisica B. Serie 12, vol. 115, no. 4, pp. 469–471, 2000. View at Google Scholar · View at MathSciNet
  13. E. C. Vagenas, “Are extremal 2D black holes really frozen?” Physics Letters B, vol. 503, no. 3-4, pp. 399–403, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. E. C. Vagenas, “Two-dimensional dilatonic black holes and Hawking radiation,” Modern Physics Letters A. Particles and Fields, Gravitation, Cosmology, Nuclear Physics, vol. 17, no. 10, pp. 609–618, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. E. C. Vagenas, “Semiclassical corrections to the Bekenstein-Hawking entropy of the BTZ black hole via self-gravitation,” Physics Letters B, vol. 533, no. 3-4, pp. 302–306, 2002. View at Publisher · View at Google Scholar
  16. A. J. M. Medved, “Radiation via tunnelling in the charged BTZ black hole,” Classical and Quantum Gravity, vol. 19, no. 3, pp. 589–598, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. A. J. M. Medved, “Radiation via tunneling from a de Sitter cosmological horizon,” Physical Review D, vol. 66, no. 12, Article ID 124009, 7 pages, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  18. L. Susskind, “The world as a hologram,” Journal of Mathematical Physics, vol. 36, no. 11, pp. 6377–6396, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. E. Verlinde, “On the holographic principle in a radiation dominated universe,” http://arxiv.org/abs/hepth/0008140.
  20. D. Birmingham and S. Mokhtari, “The Cardy-Verlinde formula and Taub-bolt-AdS spacetimes,” Physics Letters B, vol. 508, no. 3-4, pp. 365–368, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  21. D. Klemm, A. C. Petkou, and G. Siopsis, “Entropy bounds, monotonicity properties and scaling in CFTs,” Nuclear Physics B, vol. 601, no. 1-2, pp. 380–394, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. B. Wang, E. Abdalla, and R.-K. Su, “Relating Friedmann equation to Cardy formula in universes with cosmological constant,” Physics Letters B, vol. 503, no. 3-4, pp. 394–398, 2001. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  23. M. R. Setare, “The Cardy-Verlinde formula and entropy of topological Reissner-Nordström black holes in de Sitter spaces,” Modern Physics Letters A. Particles and Fields, Gravitation, Cosmology, Nuclear Physics, vol. 17, no. 32, pp. 2089–2094, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  24. M. R. Setare and M. B. Altaie, “The Cardy-Verlinde formula and entropy of topological Kerr-Newman black holes in de Sitter spaces,” The European Physical Journal C. Particles and Fields, vol. 30, no. 2, pp. 273–277, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. M. R. Setare and R. Mansouri, “Holographic thermodynamics on the brane in topological Reissner-Nordström de Sitter space,” International Journal of Modern Physics A, vol. 18, no. 24, pp. 4443–4450, 2003. View at Publisher · View at Google Scholar · View at Scopus
  26. C. O. Lee, “Cardy-Verlinde formula in Taub-NUT/bolt-(A)dS space,” Physics Letters B, vol. 670, no. 2, pp. 146–149, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  27. A. J. M. Medved, “Quantum-corrected Cardy entropy for generic (1+1)-dimensional gravity,” Classical and Quantum Gravity, vol. 19, no. 9, pp. 2503–2513, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  28. S. Mukherji and S. S. Pal, “Logarithmic corrections to black hole entropy and AdS/CFT correspondence,” Journal of High Energy Physics, vol. 2002, no. 5, article 026, 2002. View at Publisher · View at Google Scholar
  29. J. E. Lidsey, S. Nojiri, S. D. Odintsov, and S. Ogushi, “The AdS/CFT correspondence and logarithmic corrections to braneworld cosmology and the Cardy-Verlinde formula,” Physics Letters B, vol. 544, no. 3-4, pp. 337–345, 2002. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. S. Carlip, “Logarithmic corrections to black hole entropy, from the Cardy formula,” Classical and Quantum Gravity, vol. 17, no. 20, pp. 4175–4186, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  31. M. R. Setare and E. C. Vagenas, “Cardy-Verlinde formula and Achúcarro-Ortiz black hole,” Physical Review D, vol. 68, no. 6, Article ID 064014, 5 pages, 2003. View at Publisher · View at Google Scholar · View at MathSciNet
  32. M. R. Setare and E. C. Vagenas, “Self-gravitational corrections to the Cardy-Verlinde formula of the Achúcarro-Ortiz black hole,” Physics Letters B, vol. 584, no. 1-2, pp. 127–132, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  33. M. R. Setare and M. Jamil, “The Cardy-Verlinde formula and entropy of the charged rotating BTZ black hole,” Physics Letters B, vol. 681, no. 5, pp. 469–471, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  34. F. Darabi, M. Jamil, and M. R. Setare, “Self-gravitational corrections to the Cardy-Verlinde formula of charged BTZ black hole,” Modern Physics Letters A. Particles and Fields, Gravitation, Cosmology, Nuclear Physics, vol. 26, no. 14, pp. 1047–1057, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  35. G. Abbas, “Cardy-Verlinde formula of noncommutative Schwarzschild black hole,” Advances in High Energy Physics, vol. 2014, Article ID 306256, 4 pages, 2014. View at Publisher · View at Google Scholar
  36. J. Bardeen, “Non-singular general relativistic gravitational collapse,” in Proceedings of the 5th International Conference on Gravitation and the Theory of Relativity, Tbilisi Unversty Press, Tbilisi, Georgia, September 1968.
  37. E. Ayón-Beato and A. García, “New regular black hole solution from nonlinear electrodynamics,” Physics Letters B, vol. 464, no. 1-2, pp. 25–29, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  38. K. A. Bronnikov, “Comment on ‘regular black hole in general relativity coupled to nonlinear electrodynamics’,” Physical Review Letters, vol. 85, p. 4641, 2000. View at Publisher · View at Google Scholar
  39. R. Bousso, “A covariant entropy conjecture,” Journal of High Energy Physics, vol. 1999, no. 7, article 004, 1999. View at Publisher · View at Google Scholar
  40. G. 't Hooft, “Dimensional reduction in quantum gravity,” http://arxiv.org/abs/gr-qc/9310026.
  41. M. R. Setare and E. C. Vagenas, “Self-gravitational corrections to the Cardy-Verlinde formula and the FRW brane cosmology in SdS5 bulk,” International Journal of Modern Physics A, vol. 20, no. 30, pp. 7219–7232, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  42. M. R. Setare, “The generalized uncertainty principle and corrections to the Cardy-Verlinde formula in SAdS5 black holes,” International Journal of Modern Physics A, vol. 21, no. 6, p. 1325, 2006. View at Publisher · View at Google Scholar
  43. M. R. Setare, “Space noncommutativity corrections to the Cardy-Verlinde formula,” International Journal of Modern Physics A, vol. 21, no. 13-14, p. 3007, 2006. View at Publisher · View at Google Scholar
  44. M. Sharif and W. Javed, “Quantum corrections for ABGB black hole,” Astrophysics and Space Science, vol. 337, no. 1, pp. 335–341, 2012. View at Publisher · View at Google Scholar · View at Scopus