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Massless Spin–Zero Particle and the Classical Action via Hamilton–Jacobi Equation in Gödel Universe

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Abstract

In this letter we investigate the separability of the Klein–Gordon and Hamilton–Jacobi equation in Gödel universe. We show that the Klein–Gordon eigen modes are quantized and the complete spectrum of the particle’s energy is a mixture of an azimuthal quantum number, m and a principal quantum number, n and a continuous wave number k. We also show that the Hamilton–Jacobi equation gives a closed function for classical action. These results may be used to calculate the Casimir vacuum energy in Gödel universe.

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References

  1. Gödel, K.: Rev. Mod. Phys. 21, 447–450 (1949)

    Article  ADS  MATH  Google Scholar 

  2. Robertson, H.P.: Relativistic cosmology. Rev. Mod. Phys. 5, 62–90 (1933)

    Article  ADS  Google Scholar 

  3. Clifton, T., Barrow, J.D.: Phys. Rev. D 72, 123003 (2005)

    Article  MathSciNet  ADS  Google Scholar 

  4. Banados, M., Gomberoff, A.: Phys. Rev. D 73, 044006 (2006)

    Article  MathSciNet  ADS  Google Scholar 

  5. Barrow, J.D., Dabrowski, M.P.: Phys. Rev. D 58, 103502 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  6. Kanti, P., Vayonakis, C.E.: Phys. Rev. D 60, 103519 (1999)

    Article  MathSciNet  ADS  Google Scholar 

  7. Carneiro, S.: Phys. Rev. D 61, 083506 (2000)

    Article  MathSciNet  ADS  Google Scholar 

  8. Leahy, D.A.: Int. J. Theor. Phys. 21(8), 9 (1982)

    Article  MathSciNet  Google Scholar 

  9. Romano, A.E., Goebel, C.: Gen. Relativ. Gravit. 35, 1857–1863 (2003)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Chandrasekhar, S., Wright, J.P.: Proc. Natl. Acad. Sci. USA 47(3), 341–347 (1961)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. Barrow, J.D., Tsagas, C.: Class. Quantum Gravity 21, 1773 (2004)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  12. Barrow, J.D., Tsagas, C.: Phys. Rev. D 69, 064007 (2004)

    Article  MathSciNet  ADS  Google Scholar 

  13. Reboucas, M.J., Tiomno, J.: Phys. Rev. D 28, 1251 (1983)

    Article  MathSciNet  ADS  Google Scholar 

  14. Barrow, J.D., Dabrowski, M.P.: Phys. Rev. D 58, 103502 (1998)

    Article  MathSciNet  ADS  Google Scholar 

  15. Setare, M.R., Kamali, V.: Class. Quantum Gravity 28, 155006 (2011)

    Article  MathSciNet  ADS  Google Scholar 

  16. Li-Chun, Z., Hai, L., Huai-Fan, L., Ren, Z.: Chin. Phys. C 35, 339 (2011)

    Article  ADS  Google Scholar 

  17. Li, H.-L.: Chin. Phys. B 20, 030402 (2011)

    Article  ADS  Google Scholar 

  18. Saha, M., Chowdhury, A.R.: Phys. Scr. 61, 527 (2000)

    Article  ADS  MATH  Google Scholar 

  19. Gürses, M., Karasu, A., Sarioğlu, Ö.: Class. Quantum Gravity 22, 1527–1543 (2005)

    Article  ADS  MATH  Google Scholar 

  20. Gürses, M., Karasu, A., Sarioğlu, Ö.: Class. Quantum Gravity 22, 4699–4713 (2005)

    Article  MATH  Google Scholar 

  21. Gleiser, R.J., Gürses, M., Karasu, A., Sarioğlu, Ö.: Class. Quantum Gravity 23, 2653–2664 (2006)

    Article  MATH  Google Scholar 

  22. Grave, F., Buser, M., Müller, T., Wunner, G., Schleich, W.P.: Phys. Rev. D 80, 103002 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  23. Ryan, M., Shepley, L.: Homogeneous Relativistic Cosmologies. Princeton Series in Physics. Princeton U.P., Princeton (1975)

    Google Scholar 

  24. Morse, P., Feschback, H.: Methods of Theoretical Physics. McGraw-Hill, New York (1953)

    MATH  Google Scholar 

  25. Hiscock, W.A.: Phys. Rev. D 17, 1497 (1978)

    Article  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Department of Physics, Shahid Beheshti University, G.C., Evin, Tehran, 19839, Iran

    A. F. Bahrehbakhsh

  2. Eurasian International Center for Theoretical Physics, Eurasian National University, Astana, 010008, Kazakhstan

    D. Momeni & R. Myrzakulov

Authors
  1. A. F. Bahrehbakhsh
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  2. D. Momeni
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  3. R. Myrzakulov
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Correspondence to A. F. Bahrehbakhsh.

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Bahrehbakhsh, A.F., Momeni, D. & Myrzakulov, R. Massless Spin–Zero Particle and the Classical Action via Hamilton–Jacobi Equation in Gödel Universe. Int J Theor Phys 51, 2427–2432 (2012). https://doi.org/10.1007/s10773-012-1122-x

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  • DOI: https://doi.org/10.1007/s10773-012-1122-x

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