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First Law of Black Hole Thermodynamics for the Kerr–Newman Spacetime Using Foliation

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Abstract

This article follows a simpler approach (Siddiqui et al. 2011) using the foliation concept with virtual displacement of hypersurfaces near the event horizon to derive the first law of black hole thermodynamics for the Kerr–Newman black hole spacetime.

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REFERENCES

  1. A. A. Siddiqui, S. M. J. Riaz, and M. Akber,C hinese Phys. Lett. 28, 050401 (2011).

  2. R. Penrose and Floyd, Nature Physical Science 229, 177 (1971).

    Article  ADS  Google Scholar 

  3. D. Christodoulou and R. Ruffini, Phys. Rev. D 4, 3552 (1971).

    Article  ADS  Google Scholar 

  4. J. Bekenstein, Ph. D Thesis, Princeton University (1972).

  5. L. Smarr, Phys. Rev. Lett. 30, 71 (1973).

    Article  ADS  Google Scholar 

  6. T. Jacobson, Phys. Rev. Lett. 75, 1260 (1995).

    Article  ADS  MathSciNet  Google Scholar 

  7. T. Padmanabhan, Class Quantum Grav. 19, 5387 (2002); gr-qc/0204019.

  8. A. Ashtekar, Adv. Theor. Math. Phys. 6, 507 (2002).

    Article  MathSciNet  Google Scholar 

  9. T. Padmanabhan, Mod. Phys. Letts. A 17, 923 (2002); gr-qc/0202078.

    Article  ADS  Google Scholar 

  10. A. Paranjape, S. Sarkar, and T. Padmanabhan, Phys. Rev. D 74, 104015 (2006); hep-th/0607240.

  11. M. Akbar and R. G. Cai, Phys. Lett. B 635, 7 (2006); hep-th/0602156.

    Article  ADS  MathSciNet  Google Scholar 

  12. M. Akbar and R. G. Cai, Phys. Rev. D 75, 084003 (2007); hep-th/0609128.

  13. C. Eling, R. Guedens, and T. Jacobson, Phys. Rev. Lett.96, 121301 (2006).

  14. M. Akbar, Chin. Phys. Lett. 24, 1158 (2007); hep-th/0702029.

    Article  ADS  Google Scholar 

  15. M. Akbar and A. A. Siddiqui, Phys. Lett. B 656, 217 (2007).

    Article  ADS  MathSciNet  Google Scholar 

  16. R. G. Cai and L. M. Cao, Phys. Rev. D 75, 064008 (2007).

  17. G. Reeb, Actualites Sci. Indust. (1952).

    Google Scholar 

  18. C. Ehresmann, Proc. Fifth Canadian Math. Congress (1961).

  19. H. Stephani, D. Kramer, M. A. H. MacCallum, C. Hoenselaers, and E. Herlt, Exact Solutions of Einstein’s Field Equations (Cambridge University Press, 2002).

    MATH  Google Scholar 

  20. J. York, Phys. Rev. Lett. 28, 1082 (1972).

    Article  ADS  Google Scholar 

  21. F. Estabrook, H. Wahlquist, S. Christensen, B. DeWitt, and T. Siang, Phys. Rev. D 7, 2814 (1973).

    Article  ADS  Google Scholar 

  22. L. Smarr and J. W. York Jr., Phys. Rev. D 17, 2529 (1978).

    Article  ADS  MathSciNet  Google Scholar 

  23. D. M. Eardley and L. Smarr, Phys. Rev. D 19, 2239 (1978).

    Article  ADS  Google Scholar 

  24. J. E. Marsden and F. J. Tipler, Phys. Rep. 66, 109 (1980).

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Iriondo, E. Malec, and N. O. Murchadha, Phys. Rev. D 54, 4792 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  26. R. Beig and N. O. Nurchadha, Phys. Rev. D 57, 4728 (1998).

    Article  ADS  MathSciNet  Google Scholar 

  27. J. Guven and N. O. Murchadha, Phys. Rev. D 60, 104015 (1999).

  28. V. Hussain, A. Qadir, and A. A. Siddiqui, Phys. Rev. D 65, 027501 (2002); gr-qc/0110068.

  29. A. Qadir and A. A. Siddiqui, Nuovo Cim. B 117, 909 (2002).

    ADS  Google Scholar 

  30. A. Qadir and A. A. Siddiqui, Int. J. Mod. Phys. D 15, 1419 (2006).

    Article  ADS  Google Scholar 

  31. R. Beig and A. A. Siddiqui, Class. Quantum Grav. 24, 5435 (2007).

    Article  ADS  Google Scholar 

  32. A. F. Ali, Phys. Rev. D 89, 104040 (2014).

  33. A. F. Ali, M. Fizal, and M. M. Khalil, Nucl. Phys. B 894, 341 (2015).

    Article  ADS  Google Scholar 

  34. S. Gangopadhyay and A. Dutta, Europhys. Lett. 115, 50005 (2016).

    Article  ADS  Google Scholar 

  35. Y. W. Kim, S. K. Kim, and Y. J. Park, Eur. Phys. J. C 76, 557 (2016).

    Article  ADS  Google Scholar 

  36. P. Rudra, M. Faizal, and A. F. Ali, Nucl. Phys. B 909, 725 (2016).

    Article  ADS  Google Scholar 

  37. Y. Heydarzade, P. Rudra, F. Darabi, A. F. Ali, and M. Faizal, Phys. Lett. B 774, 46 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  38. S. M. J. Riaz and A. A. Siddiqui, J. Astrophys. Astron. 40, 19 (2019).

    Article  ADS  Google Scholar 

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Correspondence to Syed Muhammad Jawwad Riaz or Azad A. Siddiqui.

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Jawwad Riaz, S.M., Siddiqui, A.A. First Law of Black Hole Thermodynamics for the Kerr–Newman Spacetime Using Foliation. Gravit. Cosmol. 26, 82–85 (2020). https://doi.org/10.1134/S0202289320010119

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  • DOI: https://doi.org/10.1134/S0202289320010119

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