Skip to main content
SpringerLink
Log in

Hawking radiation of Euler–Heisenberg-adS black hole under the GUP effect

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

We study Hawking radiation produced by charged Klein–Gordon and Dirac particles as tunneling from the event horizon of the Euler-Heisenberg-anti de Sitter black hole in the presence of a generalized uncertainty effect. To obtain modified Hawking temperature we use semi-classical versions of charged Klein–Gordon and Dirac equations. We review the general properties of the black hole and its standard thermodynamics elaborately. We discuss the problem of the formation of a residual mass at a finite temperature that arises in this black hole where the volume shrinking terminates even if the Hawking radiation continues at a constant rate. We find that the first-order correction of the generalized uncertainty principle to the Klein–Gordon and Dirac equations cannot be able to solve this problem. Apart from this fact, we interpret the modified thermodynamics of the black hole from another point of view under the generalized uncertainty principle effect. We model the charge/mass ratio \(Q/M\in [0.612,0.729]\) and then calculate the standard critical Hawking temperature of Sgr A* \(T_H\in [27,24]\) fK for the Euler–Heisenberg parameter \(a/Q^2\in [0,32/7]\). Improved upper limits under the GUP corrections are \(Q/M=0.769\), \(T_{KG}=406\) fK for the KG particle and \(Q/M=0.777\), \(T_{D}=410\) fK for the Dirac particle.

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
Fig. 6

Similar content being viewed by others

Data Availability Statement

No data associated in the manuscript.

References

  1. S.W. Hawking, D.N. Page, Thermodynamics of black holes in anti-de sitter space. Commun. Math. Phys. 87(4), 577–588 (1983). https://doi.org/10.1007/BF01208266

    Article  ADS  MathSciNet  Google Scholar 

  2. A. Chamblin, R. Emparan, C.V. Johnson, R.C. Myers, Charged ads black holes and catastrophic holography. Phys. Rev. D 60(6), 064018 (1999). https://doi.org/10.1103/PhysRevD.60.064018

    Article  ADS  MathSciNet  Google Scholar 

  3. S.-W. Wei, Y.-X. Liu, Triple points and phase diagrams in the extended phase space of charged gauss-bonnet black holes in ads space. Phys. Rev. D 90(4), 044057 (2014). https://doi.org/10.1103/PhysRevD.90.044057

    Article  ADS  Google Scholar 

  4. M. Cvetic, S.S. Gubser, Phases of r-charged black holes, spinning branes and strongly coupled gauge theories. J. High Energy Phys. 1999(04), 024 (1999). https://doi.org/10.1088/1126-6708/1999/04/024

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Cvetic, S.S. Gubser, Thermodynamic stability and phases of general spinning branes. J. High Energy Phys. 1999(07), 010 (1999). https://doi.org/10.1088/1126-6708/1999/07/010

    Article  MathSciNet  MATH  Google Scholar 

  6. E. Spallucci, A. Smailagic, Maxwell’s equal-area law for charged anti-de sitter black holes. Phys. Lett. B 723(4–5), 436–441 (2013). https://doi.org/10.1016/j.physletb.2013.05.038

    Article  ADS  MathSciNet  MATH  Google Scholar 

  7. D. Kubizňák, R.B. Mann, M. Teo, Black hole chemistry: thermodynamics with lambda. Class. Quantum Gravity 34(6), 063001 (2017). https://doi.org/10.1088/1361-6382/aa5c69

    Article  ADS  MathSciNet  MATH  Google Scholar 

  8. R. Zhou, Y.-X. Liu, S.-W. Wei, Phase transition and microstructures of five-dimensional charged Gauss-Bonnet-ads black holes in the grand canonical ensemble. Phys. Rev. D 102(12), 124015 (2020). https://doi.org/10.1103/PhysRevD.102.124015

    Article  ADS  MathSciNet  Google Scholar 

  9. B. Liu, Z.-Y. Yang, R.-H. Yue, Tricritical point and solid/liquid/gas phase transition of higher dimensional ads black hole in massive gravity. Ann. Phys. 412, 168023 (2020). https://doi.org/10.1016/j.aop.2019.168023

    Article  MathSciNet  Google Scholar 

  10. D. Kubizňák, R.B. Mann, P–v criticality of charged ads black holes. J. High Energy Phys. 2012(7), 1–25 (2012). https://doi.org/10.1007/JHEP07(2012)033

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Altamirano, D. Kubizňák, R.B. Mann, Reentrant phase transitions in rotating anti-de sitter black holes. Phys. Rev. D 88(10), 101502 (2013). https://doi.org/10.1103/PhysRevD.88.101502

    Article  ADS  Google Scholar 

  12. D.C. Johnston, Advances in Thermodynamics of the van der Waals Fluid (Morgan & Claypool San Rafael, San Rafael, 2014). https://doi.org/10.1088/978-1-627-05532-1

    Book  Google Scholar 

  13. S. Kruglov, Ned-ads black holes, extended phase space thermodynamics and Joule–Thomson expansion. Nuclear Phys. B (2022). https://doi.org/10.1016/j.nuclphysb.2022.115949

    Article  MathSciNet  MATH  Google Scholar 

  14. Ö. Ökcü, E. Aydıner, Joule–Thomson expansion of the charged ads black holes. Eur. Phys. J. C 77(1), 1–7 (2017). https://doi.org/10.1140/epjc/s10052-017-4598-y

    Article  Google Scholar 

  15. J.R. Muñoz de Nova, K. Golubkov, V.I. Kolobov, J. Steinhauer, Observation of thermal hawking radiation and its temperature in an analogue black hole. Nature 569(7758), 688–691 (2019)

    Article  ADS  Google Scholar 

  16. G. Gregori, G. Marocco, S. Sarkar, R. Bingham, C. Wang, Measuring Unruh radiation from accelerated electrons. arXiv preprint arXiv:2301.06772 (2023)

  17. H.S. Nguyen, D. Gerace, I. Carusotto, D. Sanvitto, E. Galopin, A. Lemaître, I. Sagnes, J. Bloch, A. Amo, Acoustic black hole in a stationary hydrodynamic flow of microcavity polaritons. Phys. Rev. Lett. 114(3), 036402 (2015)

    Article  ADS  Google Scholar 

  18. J. Steinhauer, Observation of quantum hawking radiation and its entanglement in an analogue black hole. Nat. Phys. 12(10), 959–965 (2016)

    Article  Google Scholar 

  19. J. Drori, Y. Rosenberg, D. Bermudez, Y. Silberberg, U. Leonhardt, Observation of stimulated hawking radiation in an optical analogue. Phys. Rev. Lett. 122(1), 010404 (2019)

    Article  ADS  Google Scholar 

  20. T.G. Philbin, C. Kuklewicz, S. Robertson, S. Hill, F. Konig, U. Leonhardt, Fiber-optical analog of the event horizon. Science 319(5868), 1367–1370 (2008)

    Article  ADS  Google Scholar 

  21. J. Steinhauer, Observation of self-amplifying hawking radiation in an analogue black-hole laser. Nat. Phys. 10(11), 864–869 (2014)

    Article  Google Scholar 

  22. W. Unruh, R. Schützhold, Hawking radiation from “phase horizons’’ in laser filaments? Phys. Rev. D 86(6), 064006 (2012)

    Article  ADS  Google Scholar 

  23. P. Kraus, F. Wilczek, Effect of self-interaction on charged black hole radiance. Nucl. Phys. B 437(1), 231–242 (1995). https://doi.org/10.1016/0550-3213(94)00588-6

    Article  ADS  Google Scholar 

  24. P. Kraus, F. Wilczek, Self-interaction correction to black hole radiance. Nucl. Phys. B 433(2), 403–420 (1995). https://doi.org/10.1016/0550-3213(94)00411-7

    Article  ADS  Google Scholar 

  25. M.K. Parikh, F. Wilczek, Hawking radiation as tunneling. Phys. Rev. Lett. 85(24), 5042 (2000). https://doi.org/10.1103/PhysRevLett.85.5042

    Article  ADS  MathSciNet  MATH  Google Scholar 

  26. R. Kerner, R.B. Mann, Tunnelling, temperature, and Taub-NUT black holes. Phys. Rev. D 73(10), 104010 (2006). https://doi.org/10.1103/PhysRevD.73.104010

    Article  ADS  MathSciNet  Google Scholar 

  27. R. Kerner, R.B. Mann, Tunnelling from gödel black holes. Phys. Rev. D 75(8), 084022 (2007). https://doi.org/10.1103/PhysRevD.75.084022

    Article  ADS  MathSciNet  Google Scholar 

  28. R. Kerner, R.B. Mann, Charged fermions tunnelling from Kerr–Newman black holes. Phys. Lett. B 665(4), 277–283 (2008). https://doi.org/10.1016/j.physletb.2008.06.012

    Article  ADS  MathSciNet  MATH  Google Scholar 

  29. R. Kerner, R.B. Mann, Fermions tunnelling from black holes. Class. Quantum Gravity 25(9), 095014 (2008). https://doi.org/10.1088/0264-9381/25/9/095014

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. D.-Y. Chen, Q.-Q. Jiang, X.-T. Zu, Hawking radiation of Dirac particles via tunnelling from rotating black holes in de sitter spaces. Phys. Lett. B 665(2–3), 106–110 (2008). https://doi.org/10.1016/j.physletb.2008.05.064

    Article  ADS  MathSciNet  MATH  Google Scholar 

  31. H.-L. Li, R. Lin, L.-Y. Cheng, Tunneling radiation of Dirac particles from Lifshitz black holes in higher-derivative gravity theory. EPL (Europhysics Letters) 98(3), 30002 (2012). https://doi.org/10.1209/0295-5075/98/30002

    Article  ADS  Google Scholar 

  32. I. Sakalli, A. Ovgun, Hawking radiation of spin-1 particles from a three-dimensional rotating hairy black hole. J. Exp. Theor. Phys. 121(3), 404–407 (2015). https://doi.org/10.1134/S1063776115090113

    Article  ADS  Google Scholar 

  33. I. Sakalli, A. Övgün, Black hole radiation of massive spin-2 particles in (3+1) dimensions. Eur. Phys. J. Plus 131(6), 1–13 (2016). https://doi.org/10.1140/epjp/i2016-16184-50

    Article  MATH  Google Scholar 

  34. G. Gecim, Y. Sucu, Tunnelling of relativistic particles from new type black hole in new massive gravity. J. Cosmol. Astropart. Phys. 2013(02), 023 (2013). https://doi.org/10.1088/1475-7516/2013/02/0230

    Article  MathSciNet  Google Scholar 

  35. D. Chen, H. Wu, H. Yang, Fermion’s tunnelling with effects of quantum gravity. Adv. High Energy Phys. (2013). https://doi.org/10.1155/2013/432412

    Article  MathSciNet  MATH  Google Scholar 

  36. D. Chen, H. Wu, H. Yang, S. Yang, Effects of quantum gravity on black holes. Int. J. Mod. Phys. A 29(26), 1430054 (2014). https://doi.org/10.1142/S0217751X14300543

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. D. Chen, H.W. Wu, H. Yang, Observing remnants by fermions’ tunneling. J. Cosmol. Astropart. Phys. 2014(03), 036 (2014). https://doi.org/10.1088/1475-7516/2014/03/036

    Article  MathSciNet  Google Scholar 

  38. P. Chen, Y.C. Ong, D.-H. Yeom, Black hole remnants and the information loss paradox. Phys. Rep. 603, 1–45 (2015). https://doi.org/10.1016/j.physrep.2015.10.070

    Article  ADS  MathSciNet  Google Scholar 

  39. M. Anacleto, F. Brito, E. Passos, Quantum-corrected self-dual black hole entropy in tunneling formalism with GUP. Phys. Lett. B 749, 181–186 (2015). https://doi.org/10.1016/j.physletb.2015.07.072

    Article  ADS  MATH  Google Scholar 

  40. T.I. Singh, I.A. Meitei, K.Y. Singh, Quantum gravity effects on hawking radiation of Schwarzschild–de Sitter black holes. Int. J. Theor. Phys. 56(8), 2640–2650 (2017). https://doi.org/10.1007/s10773-017-3420-90

    Article  MATH  Google Scholar 

  41. F. Scardigli, M. Blasone, G. Luciano, R. Casadio, Modified Unruh effect from generalized uncertainty principle. Eur. Phys. J. C 78(9), 1–8 (2018). https://doi.org/10.1140/epjc/s10052-018-6209-y0

    Article  Google Scholar 

  42. W. Javed, R. Babar, A. Övgün, Hawking radiation from cubic and quartic black holes via tunneling of GUP corrected scalar and fermion particles. Mod. Phys. Lett. A 34(09), 1950057 (2019). https://doi.org/10.1142/S02177323195005730

    Article  ADS  MathSciNet  MATH  Google Scholar 

  43. S. Kanzi, I. Sakallı, Gup modified hawking radiation in bumblebee gravity. Nucl. Phys. B 946, 114703 (2019). https://doi.org/10.1016/j.nuclphysb.2019.1147030

    Article  MathSciNet  MATH  Google Scholar 

  44. G. Gecim, Y. Sucu, The GUP effect on hawking radiation of the 2+1 dimensional black hole. Phys. Lett. B 773, 391–394 (2017). https://doi.org/10.1016/j.physletb.2017.08.0530

    Article  ADS  MATH  Google Scholar 

  45. G. Gecim, Y. Sucu, The GUP effect on tunneling of massive vector bosons from the 2+1 dimensional black hole. Adv. High Energy Phys. (2018). https://doi.org/10.1155/2018/7031767

    Article  MATH  Google Scholar 

  46. G. Gecim, Y. Sucu, Quantum gravity effect on the hawking radiation of charged rotating BTZ black hole. Gen. Relativ. Gravit. 50(12), 1–15 (2018). https://doi.org/10.1007/s10714-018-2478-x

    Article  MathSciNet  MATH  Google Scholar 

  47. G. Gecim, Y. Sucu, Quantum gravity effect on the hawking radiation of spinning Dilaton black hole. Eur. Phys. J. C 79(10), 1–9 (2019). https://doi.org/10.1140/epjc/s10052-019-7400-50

    Article  Google Scholar 

  48. C. Tekincay, M. Dernek, Y. Sucu, Exotic criticality of the BTZ black hole. Eur. Phys. J. Plus 136(2), 222 (2021). https://doi.org/10.1140/epjp/s13360-021-01168-7

    Article  Google Scholar 

  49. C. Tekincay, G. Gecim, Y. Sucu, Zitterbewegung particles tunneling from Reissner–Nordström ads black hole surrounded by quintessence. EPL 135(3), 31003 (2021). https://doi.org/10.1209/0295-5075/ac1aac

    Article  ADS  Google Scholar 

  50. M. Maggiore, A generalized uncertainty principle in quantum gravity. Phys. Lett. B 304(1–2), 65–69 (1993). https://doi.org/10.1016/0370-2693(93)91401-8

    Article  ADS  MathSciNet  Google Scholar 

  51. M. Maggiore, The algebraic structure of the generalized uncertainty principle. Phys. Lett. B 319(1–3), 83–86 (1993). https://doi.org/10.1016/0370-2693(93)90785-G9

    Article  ADS  MathSciNet  Google Scholar 

  52. A. Kempf, G. Mangano, R.B. Mann, Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D 52(2), 1108 (1995). https://doi.org/10.1103/PhysRevD.52.1108

    Article  ADS  MathSciNet  Google Scholar 

  53. H. Hinrichsen, A. Kempf, Maximal localization in the presence of minimal uncertainties in positions and in momenta. J. Math. Phys. 37(5), 2121–2137 (1996). https://doi.org/10.1063/1.531501

    Article  ADS  MathSciNet  MATH  Google Scholar 

  54. A. Kempf, On quantum field theory with nonzero minimal uncertainties in positions and momenta. J. Math. Phys. 38(3), 1347–1372 (1997). https://doi.org/10.1063/1.531814

    Article  ADS  MathSciNet  MATH  Google Scholar 

  55. F. Scardigli, Generalized uncertainty principle in quantum gravity from micro-black hole gedanken experiment. Phys. Lett. B 452(1–2), 39–44 (1999). https://doi.org/10.1016/S0370-2693(99)00167-7

    Article  ADS  Google Scholar 

  56. R.J. Adler, P. Chen, D.I. Santiago, The generalized uncertainty principle and black hole remnants. Gen. Relativ. Gravit. 33(12), 2101–2108 (2001). https://doi.org/10.1023/A:1015281430411

    Article  ADS  MathSciNet  MATH  Google Scholar 

  57. S. Hossenfelder, M. Bleicher, S. Hofmann, J. Ruppert, S. Scherer, H. Stöcker, Signatures in the Planck regime. Phys. Lett. B 575(1–2), 85–99 (2003). https://doi.org/10.1016/j.physletb.2003.09.040

    Article  ADS  MATH  Google Scholar 

  58. A.F. Ali, S. Das, E.C. Vagenas, Discreteness of space from the generalized uncertainty principle. Phys. Lett. B 678(5), 497–499 (2009). https://doi.org/10.1016/j.physletb.2009.06.061

    Article  ADS  MathSciNet  Google Scholar 

  59. S. Das, E.C. Vagenas, A.F. Ali, Discreteness of space from GUP II: relativistic wave equations. Phys. Lett. B 690(4), 407–412 (2010). https://doi.org/10.1016/j.physletb.2010.05.052

    Article  ADS  Google Scholar 

  60. S. Das, E.C. Vagenas, A. Farag Ali, Erratum to “discreteness of space from GUP II: relativistic wave equations”. [Phys. Lett. B 690 (2010) 407]. Phys. Lett. B 692(5), 342 (2010). https://doi.org/10.1016/j.physletb.2010.07.025

  61. S. Hossenfelder, Can we measure structures to a precision better than the Planck length? Class. Quantum Gravity 29(11), 115011 (2012). https://doi.org/10.1088/0264-9381/29/11/115011

    Article  ADS  MathSciNet  MATH  Google Scholar 

  62. A. Tawfik, A. Diab, Generalized uncertainty principle: approaches and applications. Int. J. Modern Phys. D 23(12), 1430025 (2014). https://doi.org/10.1142/S0218271814300250

    Article  ADS  MathSciNet  MATH  Google Scholar 

  63. B. Carr, J. Mureika, P. Nicolini, Sub-planckian black holes and the generalized uncertainty principle. J. High Energy Phys. 2015(7), 1–24 (2015). https://doi.org/10.1007/JHEP07(2015)052

    Article  MathSciNet  MATH  Google Scholar 

  64. M. Fadel, M. Maggiore, Revisiting the algebraic structure of the generalized uncertainty principle. Phys. Rev. D 105(10), 106017 (2022). https://doi.org/10.1103/PhysRevD.105.106017

    Article  ADS  MathSciNet  Google Scholar 

  65. W. Heisenberg, H. Euler, Consequences of dirac theory of the positron. arXiv preprint physics/0605038 (2006)

  66. J. Schwinger, On gauge invariance and vacuum polarization. Phys. Rev. 82(5), 664 (1951)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  67. H. Yajima, T. Tamaki, Black hole solutions in Euler–Heisenberg theory. Phys. Rev. D 63(6), 064007 (2001). https://doi.org/10.1103/PhysRevD.63.064007

    Article  ADS  MathSciNet  Google Scholar 

  68. T. Karakasis, G. Koutsoumbas, A. Machattou, E. Papantonopoulos, Magnetically charged Euler–Heisenberg black holes with scalar hair. Phys. Rev. D 106(10), 104006 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  69. N. Bretón, C. Lämmerzahl, A. Macías, Rotating black holes in the Einstein–Euler–Heisenberg theory. Class. Quantum Gravity 36(23), 235022 (2019)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  70. D. Chen, C. Gao, Angular momentum and chaos bound of charged particles around Einstein–Euler–Heisenberg ads black holes. New J. Phys. 24(12), 123014 (2022)

    Article  ADS  MathSciNet  Google Scholar 

  71. N. Breton, L. López, Birefringence and quasinormal modes of the Einstein–Euler–Heisenberg black hole. Phys. Rev. D 104(2), 024064 (2021)

    Article  ADS  MathSciNet  Google Scholar 

  72. Y. Feng, W. Nie, The correspondence between shadow and the test field in a Einstein–Euler–Heisenberg black hole. Int. J. Theor. Phys. 61(9), 223 (2022)

    Article  MathSciNet  MATH  Google Scholar 

  73. X.-X. Zeng, K.-J. He, G.-P. Li, E.-W. Liang, S. Guo, QED and accretion flow models effect on optical appearance of Euler–Heisenberg black holes. Eur. Phys. J. C 82(8), 764 (2022)

    Article  ADS  Google Scholar 

  74. D. Magos, N. Breton, Thermodynamics of the Euler–Heisenberg-ads black hole. Phys. Rev. D 102(8), 084011 (2020). https://doi.org/10.1103/PhysRevD.102.084011

    Article  ADS  MathSciNet  Google Scholar 

  75. S.G. Ghosh, M. Afrin, An upper limit on the charge of the black hole sgr a* from eht observations. Astrophys. J. 944(2), 174 (2023)

    Article  ADS  Google Scholar 

  76. D. Chen, Q. Jiang, P. Wang, H. Yang, Remnants, fermions’ tunnelling and effects of quantum gravity. J. High Energy Phys. 2013(11), 1–14 (2013). https://doi.org/10.1007/JHEP11(2013)176

    Article  MathSciNet  MATH  Google Scholar 

  77. H. Dai, Z. Zhao, S. Zhang, Thermodynamic phase transition of Euler–Heisenberg-ads black hole on free energy landscape. arXiv preprint arXiv:2202.14007 (2022)

  78. Maplesoft, A division of Waterloo Maple Inc., Waterloo, Ontario: Maple 2020.2

  79. G.-R. Li, S. Guo, E.-W. Liang, High-order QED correction impacts on phase transition of the Euler–Heisenberg ads black hole. Phys. Rev. D 106(6), 064011 (2022). https://doi.org/10.1103/PhysRevD.106.064011

    Article  ADS  MathSciNet  Google Scholar 

  80. A. Chowdhury, Hawking emission of charged particles from an electrically charged spherical black hole with scalar hair. Eur. Phys. J. C 79(11), 928 (2019)

    Article  ADS  Google Scholar 

  81. K.K. Kim, W.-Y. Wen, Charge-mass ratio bound and optimization in the Parikh–Wilczek tunneling model of hawking radiation. Phys. Lett. B 731, 307–310 (2014)

    Article  ADS  MATH  Google Scholar 

Download references

Author information

Author notes

  1. Mustafa Dernek, Cavit Tekincay, Ganim Gecim, Yusuf Kucukakca and Yusuf Sucu have contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Faculty of Sciences, Akdeniz University, Antalya, Turkey

    Mustafa Dernek, Cavit Tekincay, Yusuf Kucukakca & Yusuf Sucu

  2. Department of Astronomy and Space Sciences, Faculty of Science, Ataturk University, Erzurum, Turkey

    Ganim Gecim

Authors
  1. Mustafa Dernek
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Cavit Tekincay
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ganim Gecim
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Yusuf Kucukakca
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yusuf Sucu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yusuf Sucu.

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

Dernek, M., Tekincay, C., Gecim, G. et al. Hawking radiation of Euler–Heisenberg-adS black hole under the GUP effect. Eur. Phys. J. Plus 138, 369 (2023). https://doi.org/10.1140/epjp/s13360-023-03983-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-023-03983-6

Search

Navigation