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A new explanation for statistical entropy of charged black hole

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Abstract

Using the Unruh-Verlinde temperature obtained by the idea of entropy force, we directly calculated the partition functions of Boson field in Reissner-Nordström spacetime with quantum statistical method. We obtain the expression of the black hole quantum statistical entropy. We find that the term is proportional to the area of black hole horizon and the logarithmic correction term appears. Our result is valid for flat spacetime.

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References

  1. Hawking SW. Gravitational radiation from colliding black holes. Phys Rev Lett, 1971, 26: 1344–1346

    Article  ADS  Google Scholar 

  2. Bekenstein J D. Black holes and entropy. Phys Rev D, 1973, 7: 2333–2346

    Article  MathSciNet  ADS  Google Scholar 

  3. Hawking S W. Particle creation by black holes. Commun Math Phys, 1975, 43: 199–220

    Article  MathSciNet  ADS  Google Scholar 

  4. Bekenstein J D. Generalized second law of thermodynamics in blackhole physics. Phys Rev D, 1974, 9: 3292–3300

    Article  ADS  Google Scholar 

  5. Frolov V, Novikov I. Dynamical origin of the entropy of a black hole. Phys Rev D, 1993, 48: 4545–4551

    Article  MathSciNet  ADS  Google Scholar 

  6. Callan C G, Wilczek F. On geometric entropy. Phys Lett B, 1994, 333: 55–61

    Article  MathSciNet  ADS  Google Scholar 

  7. Hochberg D, Kephart TW, York J W. Positivity of entropy in the semiclassical theory of black holes and radiation. Phys Rev D, 1993, 48: 479–484

    Article  MathSciNet  ADS  Google Scholar 

  8. Padmanaban T. Phase volume occupied by a test particle around an incipient black hole. Phys Lett A, 1989, 136: 203–205

    Article  MathSciNet  ADS  Google Scholar 

  9. Li X, Zhao Z. Entropy of a Vaidya black hole. Phys Rev D, 2000, 62: 104001

    Article  MathSciNet  ADS  Google Scholar 

  10. ’t Hooft G. On the quantum structure of a black hole. Nucl Phys B, 1985, 256: 727–745

    Article  MathSciNet  ADS  Google Scholar 

  11. Cognola G, Lecca P. Electromagnetic fields in Schwarzschild and Reissner-Nordström geometry: Quantum corrections to the black hole entropy. Phys Rev D, 1998, 57: 1108–1111

    Article  MathSciNet  ADS  Google Scholar 

  12. Cai R G, Ji J Y, Soh K S. Action and entropy of black holes in spacetimes with a cosmological constant. Class Quantum Grav, 1998,15: 2783–2794

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. Zhao R, Zhang S L. Dilatonic black hole entropy without brick walls. Gen Relat Grav, 2004, 36: 2123–2130

    Article  MATH  Google Scholar 

  14. Zhao R, Zhang S L. Statistical entropy of Kerr black hole. Int J Mod Phys D, 2002, 11: 1381–1387

    Article  ADS  MATH  Google Scholar 

  15. Solodukhin S N. Black hole entropy: Statistical mechanics agrees with thermodynamics. Phys Rev D, 1996, 54: 3900–3903

    Article  MathSciNet  ADS  Google Scholar 

  16. Solodukhin S N. Entanglement entropy of black holes and antiCde Sitter space/conformal-field-theory correspondence. Phys Rev Lett, 2006, 97: 201601

    Article  ADS  Google Scholar 

  17. Cadoni M, Melis M. Holographic entanglement entropy of the BTZ black hole. Found Phys, 2010, 40: 638–657

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. Cadoni M, Melis M. Entanglement entropy of AdS black holes. Entropy, 2010, 12: 2244–2267

    Article  MathSciNet  MATH  Google Scholar 

  19. Terashima H. Entanglement entropy of the black hole horizon. Phys Rev D, 2000, 61: 104016

    Article  MathSciNet  ADS  Google Scholar 

  20. Giovanazzi S. Entanglement entropy and mutual information production rates in acoustic black holes. Phys Rev Lett, 2011, 106: 011302

    Article  ADS  Google Scholar 

  21. Zhao R, Zhang J F, Zhang L C. Statistical entropy of Ressner-Nordstrom black hole. Nucl Phys B, 2001, 609: 247–252

    Article  MATH  Google Scholar 

  22. Zhao R, Wu Y Q, Zhang L C. Spherically symmetric black-hole entropy without brick walls. Class Quantum Grav, 2003, 20: 4885–4890

    Article  MathSciNet  MATH  Google Scholar 

  23. Ghosh A, Mitra P. Entropy in dilatonic black hole background. Phys Rev Lett, 1994, 73: 2521–2523

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. Mann R B, Tarasov L, Zeinikov A. Brick walls for black holes. Class Quantum Grav, 1992, 9: 1487–1494

    Article  ADS  Google Scholar 

  25. Kim W T, Oh J J, Park Y J. Entropy of the Randall-Sundrum black brane in the brick wall method. Phys Lett B, 2001, 512: 131–136

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. He F, Zhao Z. Statistical entropies of scalar and spinor fields in Vaidyade Sitter space-time computed by the thin-layer method. Phys Rev D, 2001, 64: 044025

    Article  MathSciNet  ADS  Google Scholar 

  27. Ge X H, Shen Y G. Entropy in the NUT-Kerr-Newman black holes due to an arbitrary spin field. Class Quantum Grav, 2003, 20: 3593–3602

    Article  MathSciNet  ADS  MATH  Google Scholar 

  28. Kim W, Kim Y W, Park Y J. Entropy of the Randall-Sundrum brane world with the generalized uncertainty principle. Phys Rev D, 2006, 74: 104001

    Article  MathSciNet  ADS  Google Scholar 

  29. Kim W, Kim Y W, Park Y J. Entropy of a charged black hole in two dimensions without cutoff. Phys Rev D, 2007, 75: 127501

    Article  MathSciNet  ADS  Google Scholar 

  30. Jing J L, Yan ML. Effect of spin on the quantum entropy of black holes. Phys Rev D, 2001, 63: 084028

    Article  MathSciNet  ADS  Google Scholar 

  31. Setare M R. Logarithmic correction to the Cardy-Verlinde formula in topological Reissner-Nordström de Sitter space. Phys Lett B, 2003, 573: 173–180

    Article  MathSciNet  ADS  MATH  Google Scholar 

  32. Setare M R. Logarithmic correction to the Cardy-Verlinde formula in Achcarro-Oritz black hole. Eur Phys J C, 2004, 33: 555–559

    Article  MathSciNet  ADS  MATH  Google Scholar 

  33. Setare M R. The generalized uncertainty principle corrections to the Cardy-Verlinde formula in SAdS5 black holes. Int JMod Phys A, 2006, 21: 1325–1332

    Article  MathSciNet  ADS  MATH  Google Scholar 

  34. Setare M R, Vagenas E C. Self-gravitational corrections to the Cardy-Verlinde formula of the Achcarro-Ortiz black hole. Phys Lett B, 2004, 584: 127–132

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. Cai R G, Cao L M, Hu Y P. Corrected entropy-area relation and modified Friedmann equations. J High Energy Phys, 2008, 08: 090

    Article  MathSciNet  ADS  Google Scholar 

  36. Lemos J P S, Zaslavskii O B. Entropy of extremal black holes from entropy of quasiblack holes. Phys Lett B, 2011, 695: 37–40

    Article  MathSciNet  ADS  Google Scholar 

  37. Ghosh T, SenGupta S. Entropy of charged dilaton-axion black hole. Phys Rev D, 2008, 78: 024045

    Article  MathSciNet  ADS  Google Scholar 

  38. Cheng I N, Okamura D, Takeuchi T. Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem. Phys Rev D, 2002, 65: 125028

    Article  ADS  Google Scholar 

  39. Setare M R. Corrections to the Cardy-Verlinde formula from the generalized uncertainty principle. Phys Rev D, 2004, 70: 087501

    Article  MathSciNet  ADS  Google Scholar 

  40. Medved A J M, Vagenas E C. When conceptual worlds collide: The generalized uncertainty principle and the Bekenstein-Hawking entropy. Phys Rev D, 2004, 70: 124021

    Article  MathSciNet  ADS  Google Scholar 

  41. Kim Y W, Park Y J. Entropy of the Schwarzschild black hole to all orders in the Planck length. Phys Lett B, 2007, 655: 172–177

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. Chatterjee A, Majumdar P. Universal canonical black hole entropy. Phys Rev Lett, 2004, 92: 141301

    Article  MathSciNet  ADS  Google Scholar 

  43. Kaul R K, Majumdar P. Logarithmic correction to the Bekenstein-Hawking entropy. Phys Rev Lett, 2000, 84: 5255–5257

    Article  MathSciNet  ADS  Google Scholar 

  44. Camellia G A, Arzano M, Procaccini A. Severe constraints on the loopquantumgravity energy-momentum dispersion relation from the blackhole area-entropy law. Phys Rev D, 2004, 70: 107501

    Article  MathSciNet  ADS  Google Scholar 

  45. Chatterjee A, Majumdar P. Mass and charge fluctuations and black hole entropy. Phys Rev D, 2005, 71: 024003

    Article  MathSciNet  ADS  Google Scholar 

  46. Myung Y S. Logarithmic corrections to three-dimensional black holes and de Sitter spaces. Phys Lett B, 2004, 579: 205–210

    Article  ADS  MATH  Google Scholar 

  47. Akbar M M, Das S. Entropy corrections for Schwarzschild and Reissner-Nordström black holes. Class Quantum Grav, 2004, 21: 1383–1392

    Article  MathSciNet  ADS  MATH  Google Scholar 

  48. Das S. General logarithmic corrections to black-hole entropy. Class Quantum Grav, 2002, 19: 2355–2368

    Article  ADS  MATH  Google Scholar 

  49. Rovelli C. Black hole entropy from loop quantum gravity. Phys Rev Lett, 1996, 77: 3288–3291

    Article  MathSciNet  ADS  MATH  Google Scholar 

  50. Ashtekar A. Quantum geometry and black hole entropy. Phys Rev Lett, 1998, 80: 904–907

    Article  MathSciNet  ADS  MATH  Google Scholar 

  51. Verlinde E P. On the origin of gravity and the laws of Newton. arXiv: 1001.1001.0785

  52. Cai R G, Cao L M, Ohta N. Friedmann equations from entropic force. Phys Rev D, 2010, 81: 061501 (R)

    ADS  Google Scholar 

  53. Cai R G, Cao L M, Ohta N. Notes on entropy force in general spherically symmetric spacetimes. Phys Rev D, 2010, 81: 084012

    Article  MathSciNet  ADS  Google Scholar 

  54. Myung Y S, Kim Y W. Entropic force and entanglement system. Phys Rev D, 2010, 81: 105012

    Article  ADS  Google Scholar 

  55. Tian Y, Wu X N. Thermodynamics of black holes from equipartition of energy and holography. Phys Rev D, 2010, 81: 104013

    Article  ADS  Google Scholar 

  56. Cai Y F, Liu J, Li H. Entropic cosmology: A unified model of inflation and late-time acceleration. Phys Lett B, 2010, 690: 213–219

    Article  ADS  Google Scholar 

  57. Chang-Young E, Eune M, Kimm K, et al. Surface gravity and Hawking temperature from entropic force viewpoint. Mod Phys Lett A, 2010, 25: 2825–2830

    Article  ADS  MATH  Google Scholar 

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  1. Institute of Theoretical Physics, Department of Physics, Shanxi Datong University, Datong, 037009, China

    Ren Zhao & LiChun Zhang

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  1. Ren Zhao
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  2. LiChun Zhang
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Correspondence to Ren Zhao.

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Zhao, R., Zhang, L. A new explanation for statistical entropy of charged black hole. Sci. China Phys. Mech. Astron. 56, 1632–1635 (2013). https://doi.org/10.1007/s11433-013-5167-5

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  • DOI: https://doi.org/10.1007/s11433-013-5167-5

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