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Killing and Noether Symmetries of Plane Symmetric Spacetime

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Abstract

This paper is devoted to investigate the Killing and Noether symmetries of static plane symmetric spacetime. For this purpose, five different cases have been discussed. The Killing and Noether symmetries of Minkowski spacetime in cartesian coordinates are calculated as a special case and it is found that Lie algebra of the Lagrangian is 10 and 17 dimensional respectively. The symmetries of Taub’s universe, anti-deSitter universe, self similar solutions of infinite kind for parallel perfect fluid case and self similar solutions of infinite kind for parallel dust case are also explored. In all the cases, the Noether generators are calculated in the presence of gauge term. All these examples justify the conjecture that Killing symmetries form a subalgebra of Noether symmetries (Bokhari et al. in Int. J. Theor. Phys. 45:1063, 2006).

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Acknowledgement

MFS is thankful to National University of Computer and Emerging Sciences (NUCES) Lahore Campus, for funding the PhD programme.

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Authors and Affiliations

  1. National University of Computer & Emerging Sciences, Lahore Campus, Pakistan

    M. Farasat Shamir & Akhlaq Ahmad Bhatti

  2. Deanship of Educational Services, Qassim University, Buraidah, Qassim, KSA

    Adil Jhangeer

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  1. M. Farasat Shamir
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  2. Adil Jhangeer
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  3. Akhlaq Ahmad Bhatti
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Correspondence to M. Farasat Shamir.

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Shamir, M.F., Jhangeer, A. & Bhatti, A.A. Killing and Noether Symmetries of Plane Symmetric Spacetime. Int J Theor Phys 52, 3106–3117 (2013). https://doi.org/10.1007/s10773-013-1602-7

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  • DOI: https://doi.org/10.1007/s10773-013-1602-7

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