Skip to main content
SpringerLink
Log in

Three-dimensional AdS black holes in massive-power-Maxwell theory

  • Research
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

Recently, it was shown that the power-Maxwell (PM) theory could remove the singularity of the electric field (B. Eslam Panah, Europhys. Lett. 134, 20005 (2021)). Motivated by a great interest in three-dimensional black holes and a surge of success in studying massive gravity from both the cosmological and astrophysical points of view, we investigate three-dimensional black hole solutions in de Rham, Gabadadze, and Tolley massive theory of gravity in the presence of PM electrodynamics. First, we extract exact three-dimensional solutions in this theory of gravity. Then we study the geometrical properties of these solutions. Calculating conserved and thermodynamic quantities, we check the validity of the first law of thermodynamics for these black holes. We also examine the stability of these black holes in the context of the canonical ensemble. We continue calculating this kind of black hole’s optical features, such as the photon orbit radius, the energy emission rate, and the deflection angle. Considering these optical quantities, finally, we analyze the effective role of the parameters of models on them.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability

This manuscript does not have any associated data.

References

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  3. Lee, H.-W., Myung, Y.-S., Kim, J.-Y.: Phys. Lett. B 466, 211 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  4. Larranaga, A.: Commun. Theor. Phys. 50, 1341 (2008)

    Article  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  6. Cai, R.-G., Cho, J.-H.: Phys. Rev. D 60, 067502 (1999)

    Article  ADS  MathSciNet  Google Scholar 

  7. Ashtekar, A., Wisniewski, J., Dreyer, O.: Adv. Theor. Math. Phys. 6, 507 (2003)

    Article  Google Scholar 

  8. Sarkar, T., Sengupta, G., Nath Tiwari, B.: J. High Energy Phys. 11, 015 (2006)

    Article  ADS  Google Scholar 

  9. Cadoni, M., Monni, C.: Phys. Rev. D 80, 024034 (2009)

    Article  ADS  Google Scholar 

  10. Cong, W., Mann, R.B.: J. High Energy Phys. 11, 004 (2019)

    Article  ADS  Google Scholar 

  11. Witten, E.: Three-Dimensional Gravity Revisited. arXiv:0706.3359

  12. Anacleto, M.A., Brito, F.A., Passos, E.: Phys. Lett. B 743, 184 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  13. Emparan, R., Horowitz, G.T., Myers, R.C.: J. High Energy Phys. 01, 021 (2000)

    Article  ADS  Google Scholar 

  14. Carlip, S.: Class. Quant. Gravit. 22, R85 (2005)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  16. Frodden, E., Geiller, M., Noui, K., Perez, A.: J. High Energy Phys. 05, 139 (2013)

    Article  ADS  Google Scholar 

  17. Singh, D.V., Siwach, S.: Class. Quant. Gravit. 30, 235034 (2013)

    Article  ADS  Google Scholar 

  18. Caputa, P., Jejjala, V., Soltanpanahi, H.: Phys. Rev. D 89, 046006 (2014)

    Article  ADS  Google Scholar 

  19. Jurić, T., Samsarov, A.: Phys. Rev. D 93, 104033 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  20. Emparan, R., Frassino, A.M., Way, B.: JHEP 11, 137 (2020)

    Article  ADS  Google Scholar 

  21. Germani, C., Procopio, G.P.: Phys. Rev. D 74, 044012 (2006)

    Article  ADS  MathSciNet  Google Scholar 

  22. de la Fuente, A., Sundrum, R.: J. High Energy Phys. 09, 073 (2014)

    Article  Google Scholar 

  23. Ziogas, V.: J. High Energy Phys. 09, 114 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  24. Henderson, L.J., Hennigar, R.A., Mann, R.B., Smith, A.R.H., Zhang, J.: Phys. Lett. B 809, 135732 (2020)

    Article  MathSciNet  Google Scholar 

  25. de Souza Campos, L., Dappiaggi, C.: Phys. Lett. B 816, 136198 (2021)

    Article  Google Scholar 

  26. Koch, B., Reyes, I.A., Rincón, A.: Class. Quant. Gravit. 33, 225010 (2016)

    Article  ADS  Google Scholar 

  27. Rincón, A., Contreras, E., Bargueno, P., Koch, B., Panotopoulos, G.: Eur. Phys, J. C 641 (2018)

  28. Fathi, M., Rincón, Á., Villanueva, J.R.: Class. Quant. Gravit. 37, 075004 (2020)

    Article  ADS  Google Scholar 

  29. Javed, W., Ali, R., Babar, R., Övgün, A.: Eur. Phys. J. Plus. 134, 511 (2019)

    Article  Google Scholar 

  30. Babar, R., Javed, W., Övgün, A.: Mod. Phys. Lett. A 35, 2050104 (2020)

    Article  ADS  Google Scholar 

  31. Emparan, R., Frassino, A.M., Way, B.: JHEP 11, 137 (2020)

    Article  ADS  Google Scholar 

  32. Cardenas, M., Fuentealba, O., Martinez, C.: Phys. Rev. D 90, 124072 (2014)

    Article  ADS  Google Scholar 

  33. Gwak, B., Lee, B.-H.: Phys. Lett. B 755, 324 (2016)

    Article  ADS  Google Scholar 

  34. Alsaleh, S.: Int. J. Mod. Phys. A 32, 1750076 (2017)

    Article  ADS  Google Scholar 

  35. Gupta, K.S., Jurić, T., Samsarov, A.: J. High Energy Phys. 06, 107 (2017)

    Article  ADS  Google Scholar 

  36. Nashed, G.G.L., Capozziello, S.: Int. J. Mod. Phys. A 33, 1850076 (2018)

    Article  ADS  Google Scholar 

  37. Eslam Panah, B., Hendi, S.H., Panahiyan, S., Hassaine, M.: Phys. Rev. D 98, 084006 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  38. Rincón, A., Koch, B.: Eur. Phys. J. C 78, 1022 (2018)

    Article  ADS  Google Scholar 

  39. Hong, S.-T., Kim, Y.-W., Park, Y.-J.: Phys. Rev. D 99, 024047 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  40. Mu, B., Tao, J., Wang, P.: Phys. Lett. B 800, 135098 (2020)

    Article  MathSciNet  Google Scholar 

  41. Cañate, P., Magos, D., Breton, N.: Phys. Rev. D 101, 064010 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  42. Hinterbichler, K.: Rev. Mod. Phys. 84, 671 (2012)

    Article  ADS  Google Scholar 

  43. de Rham, C.: Living Rev. Rel. 17, 7 (2014)

    Article  Google Scholar 

  44. Akrami, Y., Koivisto, T.S., Sandstad, M.: J. High Energy Phys. 03, 99 (2013)

    Article  ADS  Google Scholar 

  45. Akrami, Y., Hassan, S.F., Knnig, F., Schmidt-May, A., Solomon, A.R.: Phys. Lett. B 748, 37 (2015)

    Article  ADS  Google Scholar 

  46. Babichev, E., Marzola, L., Raidal, M., Schmidt-May, A., Urban, F., Veerme, H., von Strauss, M.: Phys. Rev. D 94, 084055 (2016)

    Article  ADS  Google Scholar 

  47. Babichev, E., Marzola, L., Raidal, M., Schmidt-May, A., Urban, F., Veerme, H., von Strauss, M.: J. Cosmol. Astropart. Phys. 09, 016 (2016)

    Article  ADS  Google Scholar 

  48. Panpanich, S., Burikham, P.: Phys. Rev. D 98, 064008 (2018)

    Article  ADS  Google Scholar 

  49. Eslam Panah, B., Liu, H.L.: Phys. Rev. D 99, 104074 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  50. Hendi, S.H., Bordbar, G.H., Eslam Panah, B., Panahiyan, S.: J. Cosmol. Astropart Phys. 07, 004 (2017)

    Article  ADS  Google Scholar 

  51. Xu, J., Cao, L.M., Hu, Y.P.: Phys. Rev. D 91, 124033 (2015)

    Article  ADS  Google Scholar 

  52. Hendi, S.H., Mann, R.B., Panahiyan, S., Eslam Panah, B.: Phys. Rev. D 95, 021501(R) (2017)

    Article  ADS  MathSciNet  Google Scholar 

  53. Dehghani, A., Hendi, S.H., Mann, R.B.: Phys. Rev. D 101, 084026 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  54. Eslam Panah, B., Hendi, S.H., Ong, Y.C.: Phys. Dark Universe 27, 100452 (2020)

    Article  Google Scholar 

  55. Hou, M.-S., Xu, H., Ong, Y.C.: Eur. Phys. J. C 80, 1090 (2020)

    Article  ADS  Google Scholar 

  56. de Rham, C., Gabadadze, G.: Phys. Rev. D 82, 044020 (2010)

    Article  ADS  Google Scholar 

  57. de Rham, C., Gabadadze, G., Tolley, A.J.: Phys. Rev. Lett. 106, 231101 (2011)

    Article  ADS  Google Scholar 

  58. van Dam, H., Veltman, M.: Nucl. Phys. B 22, 397 (1970)

    Article  ADS  Google Scholar 

  59. Zakharov, V.: JETP Lett. 12, 312 (1970)

    ADS  Google Scholar 

  60. Boulware, D.G., Deser, S.: Phys. Rev. D 6, 3368 (1972)

    Article  ADS  Google Scholar 

  61. Hassan, S.F., Rosen, R.A.: Phys. Rev. Lett. 108, 041101 (2012)

    Article  ADS  Google Scholar 

  62. Fierz, M., Pauli, W.: Proc. Roy. Soc. Lond. A 173, 211 (1939)

    Article  ADS  Google Scholar 

  63. Alberte, L., Khmelnitsky, A.: Phys. Rev. D 91, 046006 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  64. Zhang, H., Li, X.-Z.: Phys. Rev. D 93, 124039 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  65. Do, T.Q.: Phys. Rev. D 93, 104003 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  66. Koyama, K., Niz, G., Tasinato, G.: Phys. Rev. Lett. 107, 131101 (2011)

    Article  ADS  Google Scholar 

  67. Nieuwenhuizen, T.M.: Phys. Rev. D 84, 024038 (2011)

    Article  ADS  Google Scholar 

  68. Gruzinov, A., Mirbabayi, M.: Phys. Rev. D 84, 124019 (2011)

    Article  ADS  Google Scholar 

  69. Berezhiani, L., Chkareuli, G., de Rham, C., Gabadadze, G., Tolley, A.J.: Phys. Rev. D 85, 044024 (2012)

    Article  ADS  Google Scholar 

  70. Rosen, R.A.: J. High Energy Phys. 10, 206 (2017)

    Article  ADS  Google Scholar 

  71. Vegh, D.: Holography without translational symmetry. arXiv:1301.0537

  72. Cai, R.G., Hu, Y.P., Pan, Q.Y., Zhang, Y.L.: Phys. Rev. D 91, 024032 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  73. Hendi, S.H., Eslam Panah, B., Panahiyan, S.: J. High Energy Phys 11, 157 (2015)

    Article  ADS  Google Scholar 

  74. Hendi, S.H., Eslam Panah, B., Panahiyana, S., Liu, H., Meng, X.-H.: Phys. Lett. B 781, 40 (2018)

    Article  ADS  Google Scholar 

  75. Nam, C.H.: Gen. Relativ. Gravit. 53, 30 (2021)

    Article  ADS  Google Scholar 

  76. Zou, D.-C., Liu, Y., Yue, R.: Eur. Phys. J. C 77, 365 (2017)

    Article  ADS  Google Scholar 

  77. Hendi, S.H., Momennia, M.: J. High Energy Phys. 10, 207 (2019)

    Article  ADS  Google Scholar 

  78. Chabab, M., El Moumni, H., Iraoui, S., Masmar, K.: Eur. Phys. J. Plus. 135, 248 (2020)

    Article  Google Scholar 

  79. Zhang, M., Zou, D.-C., Yue, R.-H.: Adv. High Energy. Phys. 2017, 3819246 (2017)

    Google Scholar 

  80. Ma, Y., Zhang, Y., Zhang, L., Wu, L., Gao, Y., Cao, S., Pan, Y.: Eur. Phys. J. C 81, 42 (2021)

    Article  ADS  Google Scholar 

  81. Ma, Y.-B., Zhang, S.-X., Wu, Y., Ma, L., Cao, S.: Commun. Theor. Phys. 69, 544 (2018)

    Article  ADS  Google Scholar 

  82. Chougule, S., Dey, S., Pourhassan, B., Faizal, M.: Eur. Phys. J. C 78, 685 (2018)

    Article  ADS  Google Scholar 

  83. Yerra, P.K., Bhamidipati, C.: Int. J. Mod. Phys. A 35, 2050120 (2020)

    Article  ADS  Google Scholar 

  84. Ma, Y., Zhang, Y., Zhang, L., Wu, L., Huang, Y., Pan, Y.: Eur. Phys. J. C 80, 213 (2020)

    Article  ADS  Google Scholar 

  85. Wu, B., Wang, C., Xu, Z.-M., Yang, W.-L.: Eur. Phys. J. C 81, 626 (2021)

    Article  ADS  Google Scholar 

  86. Eslam Panah, B., Hendi, S.H.: Europhys. Lett. 125, 60006 (2019)

    Article  ADS  Google Scholar 

  87. Hendi, S.H., Eslam Panah, B., Panahiyan, S., Momennia, M.: Phys. Lett. B 772, 43 (2017)

    Article  ADS  Google Scholar 

  88. Hendi, S.H., Eslam Panah, B., Panahiyan, S.: J. High Energy Phys. 05, 029 (2016)

    Article  ADS  Google Scholar 

  89. Ghodrati, M., Kuang, X.-M., Wang, B., Zhang, C.-Y., Zhou, Y.-T.: JHEP 1909, 009 (2019)

    Article  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  91. Eslam Panah, B.: Europhys. Lett. 134, 20005 (2021)

    Article  ADS  Google Scholar 

  92. Maeda, H., Hassaine, M., Martinez, C.: Phys. Rev. D 79, 044012 (2009)

    Article  ADS  Google Scholar 

  93. Hendi, S.H., Eslam Panah, B.: Phys. Lett. B 684, 77 (2010)

    Article  ADS  MathSciNet  Google Scholar 

  94. Jing, J., Pan, Q., Chen, S.: J. High Energy Phys. 11, 045 (2011)

    Article  ADS  Google Scholar 

  95. Roychowdhury, D.: Phys. Lett. B 718, 1089 (2013)

    Article  ADS  Google Scholar 

  96. Zhang, M., Yang, Z.-Y., Zou, D.-C., Xu, W., Yue, R.-H.: Gen. Relativ. Gravit. 47, 14 (2015)

    Article  ADS  Google Scholar 

  97. Mo, J.-X., Li, G.-Q., Xu, X.-B.: Phys. Rev. D 93, 084041 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  98. Li, H.-F., Guo, X-y., Zhao, H.-H., Zhao, R.: Gen. Relativ. Gravit. 49, 111 (2017)

  99. Eslam Panah, B.: Fortschr. Phys. 71, 2300012 (2023)

    Article  MathSciNet  Google Scholar 

  100. Panotopoulos, G., Rincón, Á.: Int. J. Mod. Phys. D 27(03), 1850034 (2017)

    Article  ADS  Google Scholar 

  101. Panotopoulos, G., Rincón, A.: Phys. Rev. D 97(8), 085014 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  102. Panotopoulos, G., Rincon, A.: Int. J. Mod. Phys. D 28(01), 1950016 (2018)

    Article  ADS  Google Scholar 

  103. Dehghani, A., Hendi, S.H.: Phys. Rev. D 104, 024025 (2021)

    Article  ADS  Google Scholar 

  104. Hassan, S.F., Rosen, R.A., Schmidt-May, A.: J. High Energy Phys. 02, 026 (2012)

    Article  ADS  Google Scholar 

  105. Hassan, S.F., Rosen, R.A.: Phys. Rev. Lett. 108, 041101 (2012)

    Article  ADS  Google Scholar 

  106. Adams, A., Roberts, D.A., Saremi, O.: Phys. Rev. D 91, 046003 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  107. Emparan, R., Pedraza, J.F., Svesko, A., Tomasevic, M., Visser, M.R.: J. High Energy Phys. 11, 073 (2022)

    Article  ADS  Google Scholar 

  108. Hendi, S.H.: Gen. Relativ. Gravit. 48, 50 (2016)

    Article  ADS  Google Scholar 

  109. Carter, B.: Phys. Rev. 174, 1559 (1968)

    Article  ADS  Google Scholar 

  110. Decanini, Y., Folacci, A., Raffaelli, B.: Class. Quant. Gravit. 28, 175021 (2011)

    Article  ADS  Google Scholar 

  111. Toshmatov, B., Ahmedov, B., Stuchlik, Z.: Eur. Phys. J. C 83, 981 (2023)

    Article  ADS  Google Scholar 

  112. Jafarzade, K., Rezaei, E., Hendi, S.H.: PTEP 053E01, 2023 (2023)

    Google Scholar 

  113. Upadhyay, S., Mandal, S., Myrzakulov, Y., Myrzakulov, K.: Ann. Phys. 450, 169242 (2023)

    Article  Google Scholar 

  114. Kala, S., Nandan, H., Sharma, P., Elmardi, M.: Mod. Phys. Lett. A 36, 2150224 (2021)

    Article  ADS  Google Scholar 

  115. Gonzalez, P.A., Olivares, M., Papantonopoulos, E., Vasquez, Y.: Phys. Rev. D 101, 044018 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  116. Panotopoulos, G., Rincon, A.: Ann. Phys. 443, 168947 (2022)

    Article  Google Scholar 

  117. Cruz, N., Olivares, M., Villanueva, J.R.: Eur. Phys. J. C 73, 2485 (2013)

    Article  ADS  Google Scholar 

  118. Panotopoulos, G.: Gen. Relativ. Gravit. 52, 54 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  119. Fernando, S., Krug, D., Curry, C.: Gen. Relativ. Gravit. 35, 1243 (2003)

    Article  ADS  Google Scholar 

  120. Cruz, N., Martinez, C., Pena, L.: Class. Quant. Gravit. 11, 2731 (1994)

    Article  ADS  Google Scholar 

  121. Lu, H., Lyu, H.D.: Phys. Rev. D 101, 044059 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  122. Perlick, V., Tsupko, O.Y., Bisnovatyi-Kogan, G.S.: Phys. Rev. D 92, 104031 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  123. Wei, S.W., Liu, Y.X.: J. Cosmol. Astropart. Phys. 11, 063 (2013)

    Article  ADS  Google Scholar 

  124. Decanini, Y., Esposito-Farse, G., Folacci, A.: Phys. Rev. D 83, 044032 (2011)

    Article  ADS  Google Scholar 

  125. Chandrasekhar, S.: The Mathematical Theory of Black Holes. Oxford University Press, New York (1983)

    Google Scholar 

  126. Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. Wiley, New York (1972)

    Google Scholar 

  127. Kocherlakota, P., Rezzolla, L.: Phys. Rev. D 102, 064058 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  128. Javed, W., Abbas, J., ovgun, A.: Ann. Phys. 418, 168183 (2020)

    Article  Google Scholar 

Download references

Acknowledgements

We are grateful to the anonymous referees for the insightful comments and suggestions, which have allowed us to improve this paper significantly. BEP thanks the University of Mazandaran. Also AR acknowledges Universidad de Tarapacá for financial support. AR acknowledges financial support from the Generalitat Valenciana through PROMETEO PROJECT CIPROM/2022/13. A. R. is fund by the María Zambrano contract ZAMBRANO 21-25 (Spain).

Author information

Authors and Affiliations

  1. Department of Theoretical Physics, Faculty of Basic Sciences, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran

    B. Eslam Panah & K. Jafarzade

  2. ICRANet-Mazandaran, University of Mazandaran, P. O. Box 47416-95447, Babolsar, Iran

    B. Eslam Panah & K. Jafarzade

  3. ICRANet, Piazza della Repubblica 10, 65122, Pescara, Italy

    B. Eslam Panah

  4. Departamento de Física Aplicada, Universidad de Alicante, Campus de San Vicente del Raspeig, 03690, Alicante, Spain

    Á. Rincón

  5. Sede Esmeralda, Universidad de Tarapacá, Avda. Luis Emilio Recabarren 2477, Iquique, Chile

    Á. Rincón

Authors
  1. B. Eslam Panah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. Jafarzade
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Á. Rincón
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

BEP: Validation, Conceptualization, Software, Investigation, Writing - review & editing. KJ: Validation, Conceptualization, Software, Investigation, Writing - review & editing. AR: Conceptualization, Investigation, Writing - review & editing.

Corresponding author

Correspondence to B. Eslam Panah.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Panah, B.E., Jafarzade, K. & Rincón, Á. Three-dimensional AdS black holes in massive-power-Maxwell theory. Gen Relativ Gravit 56, 46 (2024). https://doi.org/10.1007/s10714-024-03229-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-024-03229-5

Keywords

Search

Navigation