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On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

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Abstract

Some new infinite-dimensional generalised Lie symmetries of Einstein’s field equations for perfect fluid distribution are found by using the Lie symmetry analysis. The reduced ordinary differential equations are solved to obtain new non-trivial exact solutions. The software MAPLE is used for computation and MAPLE code is given to facilitate the research in this field.

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Acknowledgements

Rajesh Kumar Gupta and Radhika thank the National Board of Higher Mathematics for financial support provided through Ref. No. 2/48(16)/2016/NBHM(R.P.)\(/\)R&D II/14982.

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Authors and Affiliations

  1. Department of Mathematics, Central University of Haryana, Mahendragarh , 123 031, India

    R K Gupta

  2. Department of Mathematics and Statistics, Central University of Punjab, Bathinda , 151 001, India

    Radhika Jain, Sachin Kumar & Divya Jyoti

Authors
  1. R K Gupta
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  2. Radhika Jain
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  3. Sachin Kumar
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  4. Divya Jyoti
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Corresponding author

Correspondence to Sachin Kumar.

Appendix A

Appendix A

MAPLE code [17, 18] for Lie symmetries:

$$\begin{aligned}&with(PDEtools){:}\\&depvar := u(x, t){:}\\&declare(u(x, t)){:}\\&alias(u = u(x, t)){:}\\&pde1 := (-2*u^{2}+1)*(diff(u, t, t)\\&\quad -(diff(u, x, x)))\\&\quad +2*u*((diff(u, t))^{2}-(diff(u, x))^{2}) = 0{:}\\&detsys:= DeterminingPDE(pde1){:}\\&pdsolve(detsys): \end{aligned}$$

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Gupta, R.K., Jain, R., Kumar, S. et al. On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution. Pramana - J Phys 95, 123 (2021). https://doi.org/10.1007/s12043-021-02162-5

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  • DOI: https://doi.org/10.1007/s12043-021-02162-5

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