Advertisement

Thermodynamics of Reissner–Nordstr\(\ddot{\mathrm{o}}\)m black holes in higher dimensions: rainbow gravity background with general uncertainty principle

  • Amritendu Haldar
  • Ritabrata BiswasEmail author
Research Article

Abstract

In this paper, we investigate the thermodynamic properties of Reissner–Nordstr\(\ddot{\mathrm{o}}\)m black holes embedded in higher (d) dimensions in the framework of rainbow gravity incorporating the effects of the generalized uncertainty principle. We also examine all the properties graphically by varying the rainbow gravity parameter \(\eta \) and the generalized uncertainty principle parameter \(\alpha \). We find the existence of remnant and critical mass of the concerned black hole. We calculate the local temperature, local internal energy and hence we analyse the thermal stability of the black hole by computing the local heat capacity. Further, we study the phase transitions of the aforesaid black hole solution under the effects of generalized uncertainty principle. From the analysis of the specific heat at the horizon, we observe that there are phase transitions for all dimensions but when we analyze the same, measured by the local observer, we find that there exist only two phase transitions.

Keywords

Rainbow gravity Generalized uncertainty principle Remnant mass Local heat capacity 

Notes

Acknowledgements

This research is supported by the project grant of Goverment of West Bengal, Department of Higher Education, Science and Technology and Biotechnology (File no:- \( ST/P/S \& T/16G-19/2017\)). AH wishes to thank the Department of Mathematics, the University of Burdwan for the research facilities provided during the work. RB thanks IUCAA, PUNE for Visiting Associateship.

References

  1. 1.
    Amati, D., Ciafaloni, M., Veneziano, G.: Phys. Lett. B 216, 41 (1898)ADSCrossRefGoogle Scholar
  2. 2.
    Rovelli, C.: Living Rev. Relativ. 1, 1 (1998)ADSCrossRefGoogle Scholar
  3. 3.
    Carlip, S.: Rep. Prog. Phys. 64, 885 (2001)ADSCrossRefGoogle Scholar
  4. 4.
    Ambjorn, J., Loll, R.: Nucl. Phys. B 536, 407 (1998)ADSCrossRefGoogle Scholar
  5. 5.
    Ambjorn, J., Jurkiewicz, J., Loll, R.: Phys. Rev. Lett. 85, 924 (2000)ADSMathSciNetCrossRefGoogle Scholar
  6. 6.
    Ambjorn, J., Jurkiewicz, J., Loll, R.: Nucl. Phys. B 610, 347 (2001)ADSCrossRefGoogle Scholar
  7. 7.
    Girelli, F., Livine, E.R., Oriti, D.: Nucl. Phys. B 708, 411 (2005)ADSCrossRefGoogle Scholar
  8. 8.
    Kostelecky, V.A., Samuel, S.: Phys. Rev. D 39, 683 (1989)ADSCrossRefGoogle Scholar
  9. 9.
    t’Hooft, G.: Class. Quan. Grav. 13, 1023 (1996)ADSCrossRefGoogle Scholar
  10. 10.
    Amelino-Camelia, G., Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., Sarkar, S.: Nature (London) 393, 763 (1998)ADSCrossRefGoogle Scholar
  11. 11.
    Gambini, R., Pullin, J.: Phys. Rev. D 59, 124021 (1999)ADSMathSciNetCrossRefGoogle Scholar
  12. 12.
    Carroll, S.M., et al.: Phys. Rev. Lett. 87, 141601 (2001)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Amelino-Camelia, G.: Int. J. Modern Phys. D 11, 35 (2002)ADSMathSciNetCrossRefGoogle Scholar
  14. 14.
    Magueijo, J., Smolin, L.: Phys. Rev. Lett. 88, 190403 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    Alfaro, J., et al.: Phys. Rev. D 65, 103509 (2002)ADSMathSciNetCrossRefGoogle Scholar
  16. 16.
    Sahlmann, H., Thiemann, T.: Class. Quan. Grav. 23, 909 (2002)ADSCrossRefGoogle Scholar
  17. 17.
    Smolin, L.: Nucl. Phys. B 742, 142 (2006)ADSCrossRefGoogle Scholar
  18. 18.
    Magueijo, J., Smolin, L.: Class. Quan. Grav. 21, 1725 (2004)ADSCrossRefGoogle Scholar
  19. 19.
    Ali, A.F., Faizal, M., Khalil, M.M.: J. High Energy Phys. 1412, 159 (2014)ADSCrossRefGoogle Scholar
  20. 20.
    Ali, A.F., Faizal, M., Khalil, M.M.: Nucl. Phys. B 894, 341 (2015)ADSCrossRefGoogle Scholar
  21. 21.
    Ali, A.F., Faizal, M., Khalil, M.M.: Phys. Lett. B 743, 295 (2015)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    Magueijo, J., Smolin, L.: Phys. Rev. D 67, 044017 (2003)ADSMathSciNetCrossRefGoogle Scholar
  23. 23.
    Hendi, S.H., Bordbar, G.H., Eslam Panah, B., Panahiyan, S.: JCAP 09, 013 (2016)ADSCrossRefGoogle Scholar
  24. 24.
    Hendi, S.H., Momennia, M., Eslam Panah, B., Panahiyan, S.: Phys. Dark. Universe 16, 26 (2017)ADSCrossRefGoogle Scholar
  25. 25.
    Adler, R.J., Chen, P., Santiago, D.I.: Gen. Relativ. Gravit. 33, 2101 (2001)ADSCrossRefGoogle Scholar
  26. 26.
    Myung, Y.S., Kim, Y.W., Park, Y.J.: Phys. Lett. B 645, 393 (2007)ADSMathSciNetCrossRefGoogle Scholar
  27. 27.
    Dutta, A., Gangopadhyay, S.: Gen. Relativ. Gravit. 46, 1747 (2014)ADSCrossRefGoogle Scholar
  28. 28.
    Gangopadhyay, S., Dutta, A., Faizal, M.: Eur. Phys. Lett. 112, 20006 (2015)ADSCrossRefGoogle Scholar
  29. 29.
    Ling, Y., Li, X., Zhang, H.B.: Mod. Phys. Lett. A 22, 2749 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    Li, H., Ling, Y., Han, X.: Class. Quan. Grav. 26, 065004 (2009)ADSCrossRefGoogle Scholar
  31. 31.
    Feng, Z.W., Yang, S.Z.: Phys. Lett. B 772, 737 (2017)ADSCrossRefGoogle Scholar
  32. 32.
    Panahiyan, S., Hendi, S.H., Raizi, N.: Nucl. Phys. B 938, 388 (2019)ADSCrossRefGoogle Scholar
  33. 33.
    Alsaleh, S.: IJMPA 32, 1750076 (2017)ADSCrossRefGoogle Scholar
  34. 34.
    Hendi, S.H., Dehghani, A., Faizal, M.: Nucl. Phys. B 914, 117 (2017)ADSCrossRefGoogle Scholar
  35. 35.
    Hendi, S.H., Panah, B.E., Panahiyan, S., Momennia, M.: EPJC 77, 647 (2017)ADSCrossRefGoogle Scholar
  36. 36.
    Hendi, S.H., Panah, B.E., Panahiyan, S., Momennia, M.: Adv. High Energy Phys. 2016, 9813582 (2016)CrossRefGoogle Scholar
  37. 37.
    Chamblin, A., Emparan, R., Jhonson, C., Myers, R.: Phys. Rev. D 60, 064018 (1999). arXiv:hep-th/9902170 ADSMathSciNetCrossRefGoogle Scholar
  38. 38.
    Bekenstein, J.D.: Phys. Rev. D 9, 3292 (1974)ADSCrossRefGoogle Scholar
  39. 39.
    Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975).  https://doi.org/10.1007/BF02345020. Erratum: Commun. Math. Phys. 46, 206 (1976)ADSMathSciNetCrossRefGoogle Scholar
  40. 40.
    Hawking, S.W.: Phys. Rev. D 13, 191 (1976)ADSCrossRefGoogle Scholar
  41. 41.
    Zhao, R., Wu, Y.Q., Zhang, L.C.: Class. Quant. Grav. 20, 4885 (2003)CrossRefGoogle Scholar
  42. 42.
    Sun, Xue-Feng, Wen-Biao, : Phys. Lett. A 19, 677 (2004)Google Scholar
  43. 43.
    Cavaglia, M., Das, S.: Class. Quan. Grav. 21, 4511 (2004)ADSCrossRefGoogle Scholar
  44. 44.
    Ali, A.F.: Phys. Rev. D 89, 104040 (2014)ADSCrossRefGoogle Scholar
  45. 45.
    Rudra, P., Biswas, R., Debnath, U.: Astrophys. Space Sci. 335, 505 (2011)ADSCrossRefGoogle Scholar
  46. 46.
    Debnath, U., Rudra, P., Biswas, R.: Astrophys. Space Sci. 339, 135 (2012)ADSCrossRefGoogle Scholar
  47. 47.
    Rudra, P., Biswas, R., Debnath, U.: Astrophys. Space Sci. 342, 557 (2012)ADSCrossRefGoogle Scholar
  48. 48.
    Rudra, P., Biswas, R., Debnath, U.: Astrophys. Space Sci. 354, 2101 (2014)CrossRefGoogle Scholar
  49. 49.
    Kim, Yong- Wan, Park, Young-Jai: Phys. Lett. B 655, 172 (2007)ADSMathSciNetCrossRefGoogle Scholar
  50. 50.
    Yoon, M., Ha, J., Kim, W.: Phys. Rev. D 76, 047501 (2007)ADSMathSciNetCrossRefGoogle Scholar
  51. 51.
    Nourcer, K.: Phys. Lett. B 646, 63 (2007)ADSMathSciNetCrossRefGoogle Scholar
  52. 52.
    Anacieto, M.A., Brito, F.A., Passos, E., Santos, W.P.: Phys. Lett. B 737, 6 (2014)ADSCrossRefGoogle Scholar
  53. 53.
    Anacieto, M.A., Brito, F.A., Passos, E.: Phys. Lett. B 749, 181 (2015)ADSCrossRefGoogle Scholar
  54. 54.
    Anacieto, M.A., Brito, F.A., Passos, E., Mota-Silva, J.C.: Adv. High Energy Phys. 2016, 8465759 (2016)Google Scholar
  55. 55.
    Haldar, A., Biswas, R.: Mod. Phys. Lett. A 33–34, 1850200 (2018)CrossRefGoogle Scholar
  56. 56.
    Ali, A.F., Faizal, M., Khalil, M.M.: Nucl. Phys. B 894, 341 (2015)ADSCrossRefGoogle Scholar
  57. 57.
    Medved, A.J.M., Vagenas, E.C.: Phys. Rev. D 70, 124021 (2004)ADSMathSciNetCrossRefGoogle Scholar
  58. 58.
    Mandal, R., Bhattacharyya, S., Gangopadhyay, S.: arXiv:1805.07005 [gr-qc]

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of PhysicsSripat Singh CollegeJiaganj, MurshidabadIndia
  2. 2.Department of MathematicsThe University of BurdwanBurdwan, Purba BurdwanIndia

Personalised recommendations