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The relativistic heat equation on flat Friedman spacetime

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Abstract

The exact solutions of the relativistic hyperbolic heat equation on a flat Friedman spacetime metric are obtained. These solutions are obtained in three cases of flat Friedman model which correspond to radiation, matter and dark energy-dominated universe models. In particular, in the dark energy-dominated universe case, a closed form solution is obtained for which, using appropriate boundary conditions, an interesting exact solution is derived. This solution suggests that the temperature of the universe drops as it expands by a scale of an exponential function.

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References

  1. A Barletta and E Zanchini Int. J. Heat Mass Transf. 40 1007 (1997)

    Article  Google Scholar 

  2. A H Bokhari, F M Mahomed and F D Zaman, J. Math. Phys.  53 043703 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  3. B Abbasi and W Craig Proc. R. Soc. A.  470 2014036 (2014)

    Article  Google Scholar 

  4. C Bai and A S Lavine J. Heat Transf. Trans. ASME.  117 256 (1995)

  5. C Minser, K Thorne and J Wheeler Gravitation (San Francisco: W H Freeman) (1973)

  6. C R Cattaneo Compte. Rend. 247 431 (1958)

  7. E R G Eckert and R M Drake Analysis of Heat and Mass Transfer (Tokyo: McGraw-Hill Kogakusha) (1972)

    MATH  Google Scholar 

  8. G Lominadze and A B Mikhailovski Zh. Eksp. Teor. Fiz.67 959, Sov. Phys. JETP49 483 (1979)

  9. J Silk Horizons of Cosmology (Templeton Press) (2009)

  10. Malcom Longair Our Evolving Universe (Cambridge: Cambridge University Press) (1996)

  11. M B Rubin Int. J. Eng. Sci.30 1665 (1992)

    Article  Google Scholar 

  12. P M Morse and H Feshback Methods of Theoretical Physics (McGraw-Hill, New York) (1953)

    Google Scholar 

  13. P Vernotte Compte. Rend. 246 3154 (1958)

    Google Scholar 

  14. Y M Ali and L C Zhang Int. J. Heat Mass Transf.48 2741 (2005)

    Article  Google Scholar 

  15. Y Mambrini Histories of Dark Matter in the Universe (Universite paris-sud, F-91405 Orsay, France) (2014)

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia

    Usamah S. Al-Ali, Ashfaque H. Bokhari & F. D. Zaman

  2. Department of Mathematics, University of Peshawar, Peshawar, Khyber Pakhtunkhwa, Pakistan

    Tahir Hussain

  3. Department of Physics, St. John Fisher College, Rochester, NY, 14618, USA

    Munawar Karim

  4. School of Mathematics, University of the Witwatersrand, Johannesburg, Wits, 2050, South Africa

    A. H. Kara

Authors
  1. Usamah S. Al-Ali
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  2. Ashfaque H. Bokhari
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  3. Tahir Hussain
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  4. Munawar Karim
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  5. A. H. Kara
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  6. F. D. Zaman
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Correspondence to A. H. Kara.

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Al-Ali, U.S., Bokhari, A.H., Hussain, T. et al. The relativistic heat equation on flat Friedman spacetime. Indian J Phys 95, 1009–1014 (2021). https://doi.org/10.1007/s12648-020-01741-3

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  • DOI: https://doi.org/10.1007/s12648-020-01741-3

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