Abstract
By the generalized uncertainty principle, the quantum corrections on Kerr-Newman black hole thermodynamics is studied. Using the modified quantum uncertainty of particles near the event horizon, the relationship between the temperature and the horizon radius for the general stationary black hole is given. Then, to ensure the relational formula having the basic physics meaning, the critical state with Planck temperature for the black hole is obtained. In addition, considering the quantum gravity effects and using the first law of black hole thermodynamics, the entropy of the charged rotating black hole is calculated and the quantum corrections including the logarithmic item to the Bekenstein-Hawking entropy are obtained. Also, in the context of the generalized uncertainty principle, the thermal capacity of Kerr-Newman black hole is obtained. Letting the thermal capacity equal zero, the black hole radiation remnant with Planck temperature is derived. It is found that, for Kerr-Newman black hole, the remnant state is consistent with the critical state. Such, using the generalized uncertainty principle, the temperature divergence at the last stage of evaporation in the traditional Kerr-Newman black hole thermodynamics is removed.
Similar content being viewed by others
References
Hawking, S.W.: Black hole explosions. Nature. 248, 30 (1974)
Hawking, S.W.: Particle creation by black holes. Commun. Math. Phys. 43, 199 (1975)
Bekenstein, J.D.: Black holes and entropy. Phys. Rev. D. 7(8), 2333 (1973)
Hawking, S.W.: Breakdown of predictability in gravitational collapse. Phys. Rev. D. 14(10), 2460 (1976)
Hawking, S.W.: Information loss in black holes. Phys. Rev. D. 72(8), 084013 (2005)
Susskind, L.: The world as a hologram. J. Math. Phys. 36(11), 6377 (1995)
Hooft, G.: The scattering matrix approach for the quantum black hole: an overview. Int. J. Mod. Phys. A. 11(26), 4688 (1996)
Bojowald, M.: Absence of a singularity in loop quantum cosmology. Phys. Rev. Lett. 86(23), 5227 (2001)
Husain, V., Winkler, O.: Singularity resolution in quantum gravity. Phys. Rev. D. 69(8), 084016 (2004)
Kiefer, C.: Quantum gravity—a short overview. In: Fauser, B., Tolksdorf, J., Zeidler, E. (eds.) Quantum Gravity, pp. 1–13. Birkhäuser, Basel (2006)
Witten, E.: Bound states of strings and p-branes. Nucl. Phys. B. 460(2), 335 (1996)
Smolin, L.: An invitation to loop quantum gravity. arXiv preprint hep-th/0408048 (2004)
Ashtekar, A., Lewandowski, J.: Background independent quantum gravity: a status report. Class.Quant. Grav. 21(15), R53 (2004)
Garay, L.J.: Quantum gravity and minimum length. Int. J. Mod. Phys. A. 10(02), 145 (1995)
Kempf, A., Mangano, G., Mann, R.B.: Hilbert space representation of the minimal length uncertainty relation. Phys. Rev. D. 52(2), 1108 (1995)
Tawfik, A.N., Diab, A.M.: Review on generalized uncertainty principle. Rep. Prog. Phys. 78(12), 126001 (2015)
Amelino-Camelia, G.: Relativity in spacetimes with short-distance structure governed by an observer-independent (Planckian) length scale. Int. J. Mod. Phys. D. 11(01), 35 (2002)
Magueijo, J., Smolin, L.: Gravity’s rainbow. Class. Quant. Grav. 21(7), 1725 (2004)
Nasseri, F.: Schwarzschild black hole in noncommutative spaces. Gen. Relativ. Gravit. 37(12), 2223 (2005)
Amelino-Camelia, G.: Quantum-spacetime phenomenology. Living Rev. Relativ. 16, 5 (2013)
Cai, R.G., Cao, L.M.: The nature of black holes (in Chinese). Chin. Sci. Bull. 61(19), 2083 (2016)
Tawfik, A.N., Diab, A.M.: Generalized uncertainty principle: approaches and applications. Int. J. Mod. Phys. D. 23(12), 1430025 (2014)
Chang, L.N., Minic, D., Okamura, N., et al.: Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem. Phys. Rev. D. 65(12), 125028 (2002)
Li, X.: Black hole entropy without brick walls. Phys. Lett. B. 540(1), 9 (2002)
Dehghani, M., Farmany, A.: Higher dimensional black hole radiation and a generalized uncertainty principle. Phys. Lett. B. 675(5), 460–462 (2009)
Dehghani, M.: Corrections to the Hawking tunneling radiation in extra dimensions. Phys. Lett. B. 749, 125 (2015)
Medved, A.J.M., Vagenas, E.C.: When conceptual worlds collide: the generalized uncertainty principle and the Bekenstein-Hawking entropy. Phys. Rev. D. 70(12), 124021 (2004)
Majumder, B.: Black hole entropy and the modified uncertainty principle: a heuristic analysis. Phys. Lett. B. 703(4), 402 (2011)
Banerjee, R., Ghosh, S.: Generalized uncertainty principle, remnant mass and singularity problem in black hole thermodynamics. Phys. Lett. B. 688(2), 224 (2010)
Li, X., Wen, X.Q.: A heuristic analysis of black hole thermodynamics with generalized uncertainty principle. J. High Energ. Phys. 2009(10), 046 (2009)
Ali, A.F., Nafie, H., Shalaby, M.: Minimal length, maximal energy and black-hole remnants. Europhys. Lett. 100(2), 20004 (2012)
Adler, R.J., Chen, P., Santiago, D.I.: The generalized uncertainty principle and black hole remnants. Gen. Relativ. Gravit. 33(12), 2101 (2001)
Gangopadhyay, S., Dutta, A., Saha, A.: Generalized uncertainty principle and black hole thermodynamics. Gen. Relativ. Gravit. 46(2), 1661 (2014)
Gangopadhyay, S., Dutta, A.: Remnant mass and entropy of black holes and modified uncertainty principle. Gen. Relativ. Gravit. 46(6), 1747 (2014)
Gangopadhyay, S., Dutta, A.: Thermodynamics of black holes and the symmetric generalized uncertainty principle. Int. J. Theor. Phys. 55(6), 2746 (2016)
Gangopadhyay, S., Dutta, A.: Black hole thermodynamics and generalized uncertainty principle with higher order terms in momentum uncertainty. Adv. High Energy Phys. 2018, 7450607 (2018)
Wu, S.P., Liu, C.Z., Cao, Q.J., et al.: The influence of the generalized uncertainty principle on Kerr black hole thermodynamics (in Chinese). Sci. Sin-Phys. Mech. Astron. 48(5), 050401 (2018)
Hossenfelder, S.: Interpretation of quantum field theories with a minimal length scale. Phys. Rev. D. 73(10), 105013 (2006)
Hossenfelder, S.: A note on quantum field theories with a minimal length scale. Class. Quant. Grav. 25(3), 038003 (2008)
Griffiths, D.J.: Introduction to Quantum Mechanics. Prentice Hall, Section 3.49, Upper Saddle River (1995)
Fan, S.J.: A new extracting formula and a new distinguishing means on the one variable cubic equation (in Chinese). J. Hainan Normal Univ. (Nat. Sci.). 2, 91 (1989)
Page, D.N.: Hawking radiation and black hole thermodynamics. New J. Phys. 7, 203 (2005)
Chen, P., Chin Ong, Y., Yeom, D.H.: Black hole remnants and the information loss paradox. Phys. Rept. 603, 1 (2015)
Myung, Y.S., Kim, Y.W., Kim, Y.J.: Quantum cooling evaporation process in regular black holes. Phys. Lett. B. 656(4–5), 221–225 (2007)
Li, X., Ling, Y., Shen, Y.G.: Singularities and the finale of black hole evaporation. Int. J. Mod. Phys. D. 22(12), 1342016 (2013)
Li, X., Ling, Y., Shen, Y.G., et al.: Generalized uncertainty principles, effective Newton constant and the regular black hole. Ann. Phys. (N.Y.). 396, 334 (2018)
Acknowledgments
Project supported by the Natural Science Foundation of Zhejiang Province of China (No. LY14A030001) and the National Natural Science Foundation of China (No. 11373020).
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Wu, S., Liu, C. The Quantum Corrections on Kerr-Newman Black Hole Thermodynamics by the Generalized Uncertainty Principle. Int J Theor Phys 59, 2681–2693 (2020). https://doi.org/10.1007/s10773-020-04468-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-020-04468-3