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Solution of the Equations of Motion for Einstein’s Field in Fractional D Dimensional Space-Time

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Abstract

As a continuation of Sadallah et al. work (M. Sadallah, S. Muslih and D. Baleanu, Equations of motion for Einstein’s field in non-integer dimensional space. Czechoslov. J. Phys. 56:323, 2006), the fractional action function S is given as an integration over fractional spatial dimension D s and fractional time D t dimension. The variational principle which minimize S leads to Euler-Lagrange equations of motion in D s +D t fractional dimensions. As an example we extend our study to obtain the equations of motion for Einstein’s field in fractional D s +D t fractional dimensions of N+1 space-time coordinates. It is shown that the time dependent solutions are single valued for only D s =4 dimensional space. Also the angular solutions are convergent for any value of D s .

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Authors and Affiliations

  1. Department of Physics, Al-Azhar University, Gaza, Israel

    Madhat Sadallah

  2. Department of Mechanical Engineering, Southern Illinois University, Carbondale, Illinois, 62901, USA

    Sami I. Muslih

Authors
  1. Madhat Sadallah
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  2. Sami I. Muslih
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Correspondence to Sami I. Muslih.

Additional information

S.I. Muslih, on leave of absence from Al-Azhar University Gaza.

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Sadallah, M., Muslih, S.I. Solution of the Equations of Motion for Einstein’s Field in Fractional D Dimensional Space-Time. Int J Theor Phys 48, 3312 (2009). https://doi.org/10.1007/s10773-009-0133-8

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  • DOI: https://doi.org/10.1007/s10773-009-0133-8

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