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Extremal black holes in the Hořava–Lifshitz gravity

  • Regular Article - Theoretical Physics
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Abstract

We study the near-horizon geometry of extremal black holes in the z=3 Hořava–Lifshitz gravity with a flow parameter λ. For λ>1/2, near-horizon geometry of extremal black holes are AdS 2×S 2 with different radii, depending on the (modified) Hořava–Lifshitz gravity. For 1/3≤λ≤1/2, the radius v 2 of S 2 is negative, which means that the near-horizon geometry is ill-defined and the corresponding Bekenstein–Hawking entropy is zero. We show explicitly that the entropy function approach does not work for obtaining the Bekenstein–Hawking entropy of extremal black holes.

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References

  1. P. Horava, Phys. Rev. D 79, 084008 (2009). arXiv:0901.3775 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  2. P. Horava, J. High Energy Phys. 0903, 020 (2009). arXiv:0812.4287 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  3. M. Visser, Phys. Rev. D 80, 025011 (2009). arXiv:0902.0590 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  4. P. Horava, Phys. Rev. Lett. 102, 161301 (2009). arXiv:0902.3657 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  5. A. Volovich, C. Wen, J. High Energy Phys. 0905, 087 (2009). arXiv:0903.2455 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  6. J. Kluson, J. High Energy Phys. 0907, 079 (2009). arXiv:0904.1343 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  7. H. Nikolic, arXiv:0904.3412 [hep-th]

  8. H. Nastase, arXiv:0904.3604 [hep-th]

  9. K.I. Izawa, arXiv:0904.3593 [hep-th]

  10. G.E. Volovik, JETP Lett. 89, 525 (2009). arXiv:0904.4113 [gr-qc]

    Article  ADS  Google Scholar 

  11. T.P. Sotiriou, M. Visser, S. Weinfurtner, Phys. Rev. Lett. 102, 251601 (2009). arXiv:0904.4464 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  12. B. Chen, Q.G. Huang, Phys. Lett. B 683, 108 (2010). arXiv:0904.4565 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  13. R.G. Cai, B. Hu, H.B. Zhang, Phys. Rev. D 80, 041501 (2009). arXiv:0905.0255 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  14. T. Nishioka, Class. Quantum Gravity 26, 242001 (2009). arXiv:0905.0473 [hep-th]

    Article  MathSciNet  Google Scholar 

  15. D. Orlando, S. Reffert, Class. Quantum Gravity 26, 155021 (2009). arXiv:0905.0301 [hep-th]

    Article  Google Scholar 

  16. C. Charmousis, G. Niz, A. Padilla, P.M. Saffin, J. High Energy Phys. 0908, 070 (2009). arXiv:0905.2579 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  17. Y.W. Kim, H.W. Lee, Y.S. Myung, Phys. Lett. B 682, 246 (2009). arXiv:0905.3423 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  18. R.A. Konoplya, Phys. Lett. B 679, 499 (2009). arXiv:0905.1523 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  19. G. Calcagni, Phys. Rev. D 81, 044006 (2010). arXiv:0905.3740 [hep-th]

    Article  ADS  Google Scholar 

  20. M. Sakamoto, Phys. Rev. D 79, 124038 (2009). arXiv:0905.4326 [hep-th]

    Article  ADS  Google Scholar 

  21. Y.S. Myung, Phys. Rev. D 81, 064006 (2010). arXiv:0906.0848 [hep-th]

    Article  ADS  Google Scholar 

  22. C. Bogdanos, E.N. Saridakis, Class. Quantum Gravity 27, 075005 (2010). arXiv:0907.1636 [hep-th]

    Article  ADS  Google Scholar 

  23. E. Kiritsis, G. Kofinas, Nucl. Phys. B 821, 467 (2009). arXiv:0904.1334 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  24. G. Calcagni, J. High Energy Phys. 0909, 112 (2009). arXiv:0904.0829 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  25. T. Takahashi, J. Soda, Phys. Rev. Lett. 102, 231301 (2009). arXiv:0904.0554 [hep-th]

    Article  ADS  Google Scholar 

  26. S. Mukohyama, J. Cosmol. Astropart. Phys. 0906, 001 (2009). arXiv:0904.2190 [hep-th]

    Article  ADS  Google Scholar 

  27. R. Brandenberger, Phys. Rev. D 80, 043516 (2009). arXiv:0904.2835 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  28. Y.S. Piao, Phys. Lett. B 681, 1 (2009). arXiv:0904.4117 [hep-th]

    Article  ADS  Google Scholar 

  29. X. Gao, arXiv:0904.4187 [hep-th]

  30. B. Chen, S. Pi, J.Z. Tang, J. Cosmol. Astropart. Phys. 0908, 007 (2009). arXiv:0905.2300 [hep-th]

    Article  ADS  Google Scholar 

  31. E.N. Saridakis, arXiv:0905.3532 [hep-th]

  32. S. Mukohyama, Phys. Rev. D 80, 064005 (2009). arXiv:0905.3563 [hep-th]

    Article  ADS  Google Scholar 

  33. M. Minamitsuji, Phys. Lett. B 684, 194 (2010). arXiv:0905.3892 [astro-ph.CO]

    Article  MathSciNet  ADS  Google Scholar 

  34. A. Wang, Y. Wu, J. Cosmol. Astropart. Phys. 0907, 012 (2009). arXiv:0905.4117 [hep-th]

    Article  ADS  Google Scholar 

  35. S. Nojiri, S.D. Odintsov, Phys. Rev. D 81, 043001 (2010). arXiv:0905.4213 [hep-th]

    Article  ADS  Google Scholar 

  36. X. Gao, Y. Wang, R. Brandenberger, A. Riotto, Phys. Rev. D 81, 083508 (2010). arXiv:0905.3821 [hep-th]

    Article  ADS  Google Scholar 

  37. M.I. Park, J. Cosmol. Astropart. Phys. 1001, 001 (2010). arXiv:0906.4275 [hep-th]

    Article  ADS  Google Scholar 

  38. S. Mukohyama, J. Cosmol. Astropart. Phys. 0909, 005 (2009). arXiv:0906.5069 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  39. A. Wang, R. Maartens, Phys. Rev. D 81, 024009 (2010). arXiv:0907.1748 [hep-th]

    Article  ADS  Google Scholar 

  40. S.S. Kim, T. Kim, Y. Kim, Phys. Rev. D 80, 124002 (2009). arXiv:0907.3093 [hep-th]

    Article  ADS  Google Scholar 

  41. H. Lu, J. Mei, C.N. Pope, Phys. Rev. Lett. 103, 091301 (2009). arXiv:0904.1595 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  42. R.G. Cai, L.M. Cao, N. Ohta, Phys. Rev. D 80, 024003 (2009). arXiv:0904.3670 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  43. R.G. Cai, Y. Liu, Y.W. Sun, J. High Energy Phys. 0906, 010 (2009). arXiv:0904.4104 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  44. E.O. Colgain, H. Yavartanoo, J. High Energy Phys. 0908, 021 (2009). arXiv:0904.4357 [hep-th]

    Article  ADS  Google Scholar 

  45. Y.S. Myung, Y.W. Kim, arXiv:0905.0179 [hep-th]

  46. A. Kehagias, K. Sfetsos, Phys. Lett. B 678, 123 (2009). arXiv:0905.0477 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  47. R.G. Cai, L.M. Cao, N. Ohta, Phys. Lett. B 679, 504 (2009). arXiv:0905.0751 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  48. A. Ghodsi, arXiv:0905.0836 [hep-th]

  49. Y.S. Myung, Phys. Lett. B 678, 127 (2009). arXiv:0905.0957 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  50. S. Chen, J. Jing, Phys. Lett. B 687, 124 (2010). arXiv:0905.1409 [gr-qc]

    Article  ADS  Google Scholar 

  51. S. Chen, J. Jing, Phys. Rev. D 80, 024036 (2009). arXiv:0905.2055 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  52. J. Chen, Y. Wang, Int. J. Mod. Phys. A 25, 1439 (2010). arXiv:0905.2786 [gr-qc]

    Article  MATH  ADS  Google Scholar 

  53. M. Botta-Cantcheff, N. Grandi, M. Sturla, arXiv:0906.0582 [hep-th]

  54. M.I. Park, J. High Energy Phys. 0909, 123 (2009). arXiv:0905.4480 [hep-th]

    Article  ADS  Google Scholar 

  55. A. Ghodsi, E. Hatefi, Phys. Rev. D 81, 044016 (2010). arXiv:0906.1237 [hep-th]

    Article  ADS  Google Scholar 

  56. A. Castillo, A. Larranaga, arXiv:0906.4380 [gr-qc]

  57. J.J. Peng, S.Q. Wu, Eur. Phys. J. C 66, 325 (2010). arXiv:0906.5121 [hep-th]

    Article  ADS  Google Scholar 

  58. D.Y. Chen, H. Yang, X.T. Zu, Phys. Lett. B 681, 463 (2009). arXiv:0910.4821 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  59. D. Capasso, A.P. Polychronakos, Phys. Rev. D 81, 084009 (2010). arXiv:0911.1535 [hep-th]

    Article  ADS  Google Scholar 

  60. B.R. Majhi, Phys. Lett. B 686, 49 (2010). arXiv:0911.3239 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  61. R.G. Cai, A. Wang, Phys. Lett. B 686, 166 (2010). arXiv:1001.0155 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  62. F.S.N. Lobo, T. Harko, Z. Kovacs, arXiv:1001.3517 [gr-qc]

  63. S.W. Wei, Y.X. Liu, Y.Q. Wang, H. Guo, arXiv:1002.1550 [hep-th]

  64. Y.S. Myung, arXiv:1002.4448 [hep-th]

  65. G. Koutsoumbas, E. Papantonopoulos, P. Pasipoularides, M. Tsoukalas, arXiv:1004.2289 [hep-th]

  66. Y.S. Myung, Phys. Lett. B 685, 318 (2010). arXiv:0912.3305 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  67. M. Wang, J. Jing, C. Ding, S. Chen, Phys. Rev. D 81, 083006 (2010). arXiv:0912.4832 [gr-qc]

    Article  ADS  Google Scholar 

  68. J. Greenwald, A. Papazoglou, A. Wang, arXiv:0912.0011 [hep-th]

  69. E. Kiritsis, G. Kofinas, J. High Energy Phys. 1001, 122 (2010). arXiv:0910.5487 [hep-th]

    Article  Google Scholar 

  70. R.L. Arnowitt, S. Deser, C.W. Misner, in Gravitation: An Introduction to Current Research, ed. by L. Witten (Wiley, New York, 1962), pp. 227–265. Chap. 7, arXiv:gr-qc/0405109

    Google Scholar 

  71. Y.S. Myung, Phys. Lett. B 684, 158 (2010). arXiv:0908.4132 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  72. A. Sen, J. High Energy Phys. 0509, 038 (2005). arXiv:hep-th/0506177

    Article  ADS  Google Scholar 

  73. T.P. Sotiriou, M. Visser, S. Weinfurtner, J. High Energy Phys. 0910, 033 (2009). arXiv:0905.2798 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  74. D. Blas, O. Pujolas, S. Sibiryakov, J. High Energy Phys. 0910, 029 (2009). arXiv:0906.3046 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  75. K. Koyama, F. Arroja, J. High Energy Phys. 1003, 061 (2010). arXiv:0910.1998 [hep-th]

    Article  Google Scholar 

  76. D. Blas, O. Pujolas, S. Sibiryakov, arXiv:0909.3525 [hep-th]

  77. A. Papazoglou, T.P. Sotiriou, Phys. Lett. B 685, 197 (2010). arXiv:0911.1299 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  78. D. Blas, O. Pujolas, S. Sibiryakov, arXiv:0912.0550 [hep-th]

  79. I. Kimpton, A. Padilla, arXiv:1003.5666 [hep-th]

  80. M. Li, Y. Pang, J. High Energy Phys. 0908, 015 (2009). arXiv:0905.2751 [hep-th]

    MathSciNet  ADS  Google Scholar 

  81. M. Henneaux, A. Kleinschmidt, G.L. Gomez, Phys. Rev. D 81, 064002 (2010). arXiv:0912.0399 [hep-th]

    Article  ADS  Google Scholar 

  82. J. Bellorin, A. Restuccia, arXiv:1004.0055 [hep-th]

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Authors and Affiliations

  1. Institute of Basic Science and School of Computer Aided Science, Inje University, Gimhae, 621-749, Korea

    Hyung Won Lee, Yong-Wan Kim & Yun Soo Myung

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  1. Hyung Won Lee
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  2. Yong-Wan Kim
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  3. Yun Soo Myung
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Correspondence to Yun Soo Myung.

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Lee, H.W., Kim, YW. & Myung, Y.S. Extremal black holes in the Hořava–Lifshitz gravity. Eur. Phys. J. C 68, 255–263 (2010). https://doi.org/10.1140/epjc/s10052-010-1344-0

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  • DOI: https://doi.org/10.1140/epjc/s10052-010-1344-0

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