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Asymptotically charged BTZ black holes in gravity’s rainbow

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Abstract

Motivated by the wide applications of BTZ black holes and interesting results of gravity’s rainbow, we consider three dimensional rainbow solutions and investigate their thermodynamic properties. In addition to investigate black holes thermodynamics related to AdS/CFT correspondence, one may regard gravity’s rainbow to encode quantum gravity effects into the black hole solutions. We take into account the various models of linear and nonlinear electrodynamics and study their effects on the gravity’s rainbow spacetime. We also examine thermal stability and find that obtained three dimensional rainbow black holes are thermally stable.

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References

  1. Awad, A., Ali, A.F., Majumder, B.: JCAP 1310, 052 (2013)

    Article  ADS  Google Scholar 

  2. Ashour, A., Faizal, M., Ali, A. F., Hammad, F.: arXiv:1602.04926

  3. Ali, A.F., Faizal, M., Majumder, B.: Europhys. Lett. 109, 20001 (2015)

    Article  Google Scholar 

  4. Ali, A.F., Khalil, M.M.: Europhys. Lett. 110, 20009 (2015)

    Article  Google Scholar 

  5. Ali, A.F., Faizal, M., Khalil, M.M.: JHEP 1412, 159 (2014)

    Article  ADS  Google Scholar 

  6. Ali, A.F., Faizal, M., Khalil, M.M.: Nucl. Phys. B 894, 341 (2015)

    Article  ADS  Google Scholar 

  7. Ali, A.F., Faizal, M., Majumder, B., Mistry, R.: Int. J. Geom. Methods Mod. Phys. 12, 1550085 (2015)

    Article  MathSciNet  Google Scholar 

  8. Ali, A.F., Faizal, M., Khalil, M.M.: Phys. Lett. B 743, 295 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  9. Kostelecky, V.A., Samuel, S.: Phys. Rev. D 39, 683 (1989)

    Article  ADS  Google Scholar 

  10. Gambini, R., Pullin, J.: Phys. Rev. D 59, 124021 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  11. Carroll, S.M., Harvey, J.A., Kostelecky, V.A., Lane, C.D., Okamoto, T.: Phys. Rev. Lett. 87, 141601 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  12. Amelino-Camelia, G., Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., Sarkar, S.: Nature 393, 763 (1998)

    Article  ADS  Google Scholar 

  13. Hooft, G’t: Class. Quantum Gravity 13, 1023 (1996)

    Article  ADS  Google Scholar 

  14. Garattini, R., Saridakis, E.N.: Eur. Phys. J. C 75, 343 (2015)

    Article  ADS  Google Scholar 

  15. Mukohyama, S.: JHEP 0705, 048 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  16. Horava, P.: Phys. Rev. D 79, 084008 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  17. Horava, P.: Phys. Rev. Lett. 102, 161301 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  18. Amelino-Camelia, G.: Int. J. Mod. Phys. D 11, 35 (2002)

    Article  ADS  MathSciNet  Google Scholar 

  19. Magueijo, J., Smolin, L.: Phys. Rev. Lett. 88, 190403 (2002)

    Article  ADS  Google Scholar 

  20. Faizal, M.: Int. J. Geom. Methods Mod. Phys. 12, 1550022 (2015)

    Article  MathSciNet  Google Scholar 

  21. Faizal, M., Ali, A.F., Nassar, A.: J. Mod. Phys. A 30, 1550183 (2015)

    Article  ADS  Google Scholar 

  22. Ali, A.F., Faizal, M., Khalil, M.M.: JCAP 1509, 025 (2015)

    Article  MathSciNet  Google Scholar 

  23. Faizal, M., Majumder, B.: Ann. Phys. 357, 49 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. Pramanik, S., Moussa, M., Faizal, M., Ali, A.F.: Ann. Phys. 362, 24 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  25. Mohammadi, A., Ali, A.F., Golanbari, T., Aghamohammadi, A., Saaidi, Kh., Faizal, M.: arXiv:1505.04392

  26. Faizal, M., Kruglov, S.I.: Int. J. Mod. Phys. D 25, 1650013 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  27. Tawfik, A.N., El Dahab, E.A.: Int. J. Mod. Phys. A 30, 1550030 (2015)

    Article  ADS  Google Scholar 

  28. Gangopadhyay, S., Dutta, A., Faizal, M.: Europhys. Lett. 112, 20006 (2015)

    Article  ADS  Google Scholar 

  29. Bargueno, P., Vagenas, E.C.: Phys. Lett. B 742, 15 (2015)

    Article  ADS  Google Scholar 

  30. Carr, B., Mureika, J., Nicolini, P.: JHEP 1507, 05 (2015)

    ADS  Google Scholar 

  31. Hammad, F.: Phys. Rev. D 92, 044004 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  32. Faizal, M., Mandal, B.P.: Gravit. Cosmol. 21, 270 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  33. Faizal, M., Khalil, M.M., Das, S.: Eur. Phys. J. C 76, 30 (2016)

    Article  ADS  Google Scholar 

  34. Amati, D., Ciafaloni, M., Veneziano, G.: Phys. Lett. B 216, 41 (1989)

    Article  ADS  Google Scholar 

  35. Garay, L.J.: Int. J. Mod. Phys. A 10, 145 (1995)

    Article  ADS  Google Scholar 

  36. Ali, A.F., Das, S., Vagenas, E.C.: Phys. Lett. B 678, 497 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  37. Ali, A.F., Das, S., Vagenas, E.C.: Phys. Rev. D 84, 044013 (2011)

    Article  ADS  Google Scholar 

  38. Magueijo, J., Smolin, L.: Class. Quantum Gravit. 21, 1725 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  39. Garattini, R., Mandanici, G.: Phys. Rev. D 85, 023507 (2012)

    Article  ADS  Google Scholar 

  40. Leiva, C., Saavedra, J., Villanueva, J.: Mod. Phys. Lett. A 24, 1443 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  41. Li, H., Ling, Y., Han, X.: Class. Quantum Gravit. 26, 065004 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  42. Ali, A.F.: Phys. Rev. D 89, 104040 (2014)

    Article  ADS  Google Scholar 

  43. Barrow, J.D., Magueijo, J.: Phys. Rev. D 88, 103525 (2013)

    Article  ADS  Google Scholar 

  44. Liu, C.Z., Zhu, J.Y.: Gen. Relativ. Gravit. 40, 1899 (2008)

    Article  ADS  Google Scholar 

  45. Hendi, S.H., Faizal, M.: Phys. Rev. D 92, 044027 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  46. Amelino-Camelia, G., Ellis, J.R., Mavromatos, N., Nanopoulos, D.V.: Int. J. Mod. Phys. A 12, 607 (1997)

    Article  ADS  MathSciNet  Google Scholar 

  47. Amelino-Camelia, G.: Living Rev. Relativ. 16, 5 (2013)

    Article  ADS  Google Scholar 

  48. Banados, M., Teitelboim, C., Zanelli, J.: Phys. Rev. Lett. 69, 1849 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  49. Banados, M., Henneaux, M., Teitelboim, C., Zanelli, J.: Phys. Rev. D 48, 1506 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  50. Carlip, S.: Class. Quantum Gravit. 12, 2853 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  51. Witten, E.: Adv. Theor. Math. Phys. 2, 505 (1998)

    Article  MathSciNet  Google Scholar 

  52. Ashtekar, A., Wisniewski, J., Dreyer, O.: Adv. Theor. Math. Phys. 6, 507 (2002)

    Article  MathSciNet  Google Scholar 

  53. Carlip, S.: Class. Quantum Gravit. 22, R85 (2005)

    Article  ADS  MathSciNet  Google Scholar 

  54. Sarkar, T., Sengupta, G., Nath Tiwari, B.: JHEP 0611, 015 (2006)

    Article  ADS  Google Scholar 

  55. Setare, M.R.: Eur. Phys. J. C 49, 865 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  56. Witten, E.: arXiv:0706.3359

  57. Ma, M.S., Zhao, R.: Phys. Rev. D 89, 044005 (2014)

    Article  ADS  Google Scholar 

  58. Moon, T., Myung, Y.S.: Phys. Rev. D 88, 124014 (2013)

    Article  ADS  Google Scholar 

  59. Lemos, J.P.S., Quinta, G.M.: Phys. Rev. D 89, 084051 (2014)

    Article  ADS  Google Scholar 

  60. Bravo-Gaete, M., Hassaine, M.: Phys. Rev. D 90, 024008 (2014)

    Article  ADS  Google Scholar 

  61. Mertens, T.G., Verschelde, H., Zakharov, V.I.: JHEP 1406, 156 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  62. Shu, F.W., Lin, K., Wang, A., Wu, Q.: JHEP 1404, 056 (2014)

    Article  ADS  Google Scholar 

  63. Singh, D.V.: Int. J. Mod. Phys. D 24, 1550001 (2015)

    Article  ADS  Google Scholar 

  64. Herrera, Y., Hurovich, V., Santillan, O., Simeone, C.: Phys. Rev. D 92, 085042 (2015)

    Article  ADS  Google Scholar 

  65. Lemos, J.P.S., Lopes, F.J., Minamitsuji, M., Rocha, Jorge V.: Phys. Rev. D 92, 064012 (2015)

    Article  ADS  Google Scholar 

  66. Hendi, S.H.: Eur. Phys. J. C 71, 1551 (2011)

    ADS  Google Scholar 

  67. Hendi, S.H.: Prog. Theor. Phys. 127, 907 (2012)

    Article  ADS  Google Scholar 

  68. Hendi, S.H.: Int. J. Theor. Phys. 53, 4170 (2014)

    Article  MathSciNet  Google Scholar 

  69. Hendi, S.H., Eslam Panah, B., Saffari, R.: Int. J. Mod. Phys. D 23, 1450088 (2014)

    Article  ADS  Google Scholar 

  70. Sheykhi, A., Hendi, S.H., Salarpour, S.: Phys. Scr. 89, 105003 (2014)

    Article  ADS  Google Scholar 

  71. Hendi, S.H., Panahiyan, S., Eslam Panah, B.: Adv. High Energy Phys. 2015, 743086 (2015)

    Article  Google Scholar 

  72. Hendi, S.H., Panahiyan, S., Mamasani, R.: Gen. Relativ. Gravit. 47, 91 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  73. Leiva, C., Espinoza, I.: arXiv:1006.2406

  74. Born, M., Infeld, L.: Proc. R. Soc. Lond. A 144, 425 (1934)

    Article  ADS  Google Scholar 

  75. Soleng, H.H.: Phys. Rev. D 52, 6178 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  76. Hendi, S.H.: JHEP 1203, 065 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  77. Hendi, S.H.: Ann. Phys. 333, 282 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  78. Hendi, S.H.: Ann. Phys. 346, 42 (2014)

    Article  ADS  MathSciNet  Google Scholar 

  79. Hassaine, M., Martinez, C.: Phys. Rev. D 75, 027502 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  80. Hendi, S.H., Rastegar-Sedehi, H.R.: Gen. Relativ. Gravit. 41, 1355 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  81. Hendi, S.H.: Phys. Lett. B 677, 123 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  82. Hassaine, M., Martinez, C.: Class. Quantum Gravit. 25, 195023 (2008)

    Article  ADS  MathSciNet  Google Scholar 

  83. Hendi, S.H.: Prog. Theor. Phys. 124, 493 (2010)

    Article  ADS  Google Scholar 

  84. Hendi, S.H.: Eur. Phys. J. C 69, 281 (2010)

    Article  ADS  Google Scholar 

  85. Hendi, S.H.: Phys. Rev. D 82, 064040 (2010)

    Article  ADS  Google Scholar 

  86. Delphenich, D.H.: arXiv:hep-th/0309108

  87. Delphenich, D.H.: arXiv:hep-th/0610088

  88. Altshuler, B.L.: Class. Quantum Gravit. 7, 189 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  89. Fradkin, E.S., Tseytlin, A.A.: Phys. Lett. B 163, 123 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  90. Matsaev, R.R., Rahmanov, M.A., Tseytlin, A.A.: Phys. Lett. B 193, 207 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  91. Kats, Y., Motl, L., Padi, M.: JHEP 0712, 068 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  92. Cai, R.G., Nie, Z.Y., Sun, Y.W.: Phys. Rev. D 78, 126007 (2008)

    Article  ADS  Google Scholar 

  93. Ritz, A., Delbourgo, R.: Int. J. Mod. Phys. A 11, 253 (1996)

    Article  ADS  Google Scholar 

  94. Boillat, G.: J. Math. Phys. 11, 941 (1970)

    Article  ADS  Google Scholar 

  95. Boillat, G.: J. Math. Phys. 11, 1482 (1970)

    Article  ADS  Google Scholar 

  96. Gibbons, G.W., Rasheed, D.A.: Nucl. Phys. B 454, 185 (1995)

    Article  ADS  MathSciNet  Google Scholar 

  97. Heisenberg, W., Euler, H.: Z. Phys. 98, 714 (1936)

    Article  ADS  Google Scholar 

  98. Jing, J., Chen, S.: Phys. Lett. B 686, 68 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  99. Gregory, R., Kanno, S., Soda, J.: JHEP 0910, 010 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  100. Pan, Q.Y., Wang, B., Papantonopoulos, E., Oliveira, J., Pavan, A.: Phys. Rev. D 81, 106007 (2010)

    Article  ADS  Google Scholar 

  101. Dey, S., Lala, A.: Ann. Phys. 354, 165 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  102. Zhao, Z., Pan, Q., Chen, S., Jing, J.: Nucl. Phys. B 871, 98 (2013)

    Article  ADS  MathSciNet  Google Scholar 

  103. Hendi, S.H.: Phys. Lett. B 690, 220 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  104. Jing, J., Pan, Q., Chen, S.: JHEP 1111, 045 (2011)

    Article  ADS  Google Scholar 

  105. Hendi, S.H., Vahidinia, M.H.: Phys. Rev. D 88, 084045 (2013)

    Article  ADS  Google Scholar 

  106. Corless, R.M., Gonnet, G.H., Hare, D.E.G., Jeffrey, D.J., Knuth, D.E.: Adv. Comput. Math. 5, 329 (1996)

    Article  MathSciNet  Google Scholar 

  107. Bekenstein, J.D.: Lett. Nuovo Cim. 4, 737 (1972)

    Article  ADS  Google Scholar 

  108. Bekenstein, J.D.: Phys. Rev. D 7, 2333 (1973)

    Article  ADS  MathSciNet  Google Scholar 

  109. Hawking, S.W., Hunter, C.J.: Phys. Rev. D 59, 044025 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  110. Cvetic, M., Gubser, S.S.: JHEP 9904, 024 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  111. Caldarelli, M.M., Cognola, G., Klemm, D.: Class. Quantum Gravit. 17, 399 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  112. Gubser, S.S., Mitra, I.: JHEP 0108, 018 (2001)

    Article  ADS  MathSciNet  Google Scholar 

  113. Ling, Y., Li, X., Zhang, H.: Mod. Phys. Lett. A 22, 2749 (2007)

    Article  ADS  MathSciNet  Google Scholar 

  114. Gim, Y., Kim, W.: JCAP 1410, 003 (2014)

    Article  ADS  Google Scholar 

  115. Mu, B., Wang, P., Yang, H.: JCAP 1511, 045 (2015)

    Article  ADS  MathSciNet  Google Scholar 

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Acknowledgments

We are indebted to Mir Faizal for useful discussions and S. Panahiyan for reading the manuscript. We also wish to thank Shiraz University Research Council. This work has been supported financially by Research Institute for Astronomy and Astrophysics of Maragha.

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  1. Physics Department and Biruni Observatory, College of Sciences, Shiraz University, Shiraz, 71454, Iran

    S. H. Hendi

  2. Research Institute for Astrophysics and Astronomy of Maragha (RIAAM), P.O. Box 55134-441, Maragha, Iran

    S. H. Hendi

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  1. S. H. Hendi
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Hendi, S.H. Asymptotically charged BTZ black holes in gravity’s rainbow. Gen Relativ Gravit 48, 50 (2016). https://doi.org/10.1007/s10714-016-2044-3

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