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Generalized Invariant Solutions for Spherical Symmetric Non-conformally Flat Fluid Distributions of Embedding Class One

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Abstract

In the present article, using the Lie group of transformations technique all the invariant solutions of Einstein’s field equations for non-conformally flat perfect fluid spheres of embedding class one have been derived by considering a 5-flat space. The same problem for conformally flat case was tackled by Thakadiyil and Jasim (Int. J. Theor. Phys. 52:3960, 2013) using the same technique but with the lesser number of symmetries and hence could obtain only lesser number of solutions as compared to the number of solutions in this paper. All the solutions thus obtained have been subjected to reality conditions. As far as the authors are aware some of the solutions are new.

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Acknowledgements

Author is grateful to the Babasaheb Bhimrao Ambedkar University (A Central University), Lucknow for providing all the necessary facility. The author also would like to express their sincere thanks to Assistant Professor Dr. Pratibha, Department of Mathematics, I.I.T. Roorkee, Roorkee, for his valuable motivation and suggestions. Authors are highly obliged to the anonymous reviewers for their valuable suggestions and comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, School for Physical Sciences, Babasaheb Bhimrao Ambedkar University (A Central University), Lucknow, 226025, India

    Sachin Kumar

  2. Department of Applied Science, School of Engineering and Technology, Sharda University, Noida, 201306, U.P., India

    Y. K. Gupta

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  1. Sachin Kumar
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  2. Y. K. Gupta
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Correspondence to Sachin Kumar.

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Kumar, S., Gupta, Y.K. Generalized Invariant Solutions for Spherical Symmetric Non-conformally Flat Fluid Distributions of Embedding Class One. Int J Theor Phys 53, 2041–2050 (2014). https://doi.org/10.1007/s10773-014-2010-3

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  • DOI: https://doi.org/10.1007/s10773-014-2010-3

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