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Symmetry 2019, 11(2), 220; https://doi.org/10.3390/sym11020220

The Second-Order Correction to the Energy and Momentum in Plane Symmetric Gravitational Waves Like Spacetimes

Department of Mathematics, Kohat University of Science and Technology, Kohat 26000, Pakistan
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Received: 5 December 2018 / Revised: 18 January 2019 / Accepted: 22 January 2019 / Published: 13 February 2019
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Abstract

This research provides second-order approximate Noether symmetries of geodetic Lagrangian of time-conformal plane symmetric spacetime. A time-conformal factor is of the form e ϵ f ( t ) which perturbs the plane symmetric static spacetime, where ϵ is small a positive parameter that produces perturbation in the spacetime. By considering the perturbation up to second-order in ϵ in plane symmetric spacetime, we find the second order approximate Noether symmetries for the corresponding Lagrangian. Using Noether theorem, the corresponding second order approximate conservation laws are investigated for plane symmetric gravitational waves like spacetimes. This technique tells about the energy content of the gravitational waves. View Full-Text
Keywords: Einstein field equations; time conformal spacetime; approximate conservation of energy Einstein field equations; time conformal spacetime; approximate conservation of energy
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Ali, M.; Ali, F.; Saboor, A.; Ghafar, M.S.; Khan, A.S. The Second-Order Correction to the Energy and Momentum in Plane Symmetric Gravitational Waves Like Spacetimes. Symmetry 2019, 11, 220.

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