Positive energy condition for LRS Bianchi type-II spacetimes via Noether symmetries
Muhammad Hammad Waheed
1,*
,
Ibrar Hussain
2
1 Department of Basic Sciences, College of Electrical and Mechanical Engineering, National University of Science and Technology , H-12 campus, Islamabad 44000, Pakistan
2 Department of Humanities and Sciences, School of Electrical Engineering and Computer Science, National University of Science and Technology , H-12 campus, Islamabad 44000, Pakistan
Abstract
In this paper, we investigate the locally rotationally symmetric Bianchi type-II spacetimes by employing the Noether and Lie symmetry approaches. Different choices of the scale factors are considered, and the corresponding symmetry algebras together with their first integrals are explicitly constructed. It is shown that the general case admits a three-dimensional Noether algebra, which extends to higher dimensions for particular functional forms of the scale factors, while the Lie symmetry algebra ranges from six to eight dimensions. The conserved quantities obtained through Noether symmetries provide important tools to simplify the dynamics of the system. In addition, the curvature characteristics are studied through the Ricci scalar and Einstein tensor, where the analysis of the \(\mathcal{G}_{00}\) component of the Einstein tensor confirms the positivity of the energy density. This establishes that the obtained cosmological models are physically realistic.
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Cite this article
Waheed, M. H. and Hussain, I., Positive energy condition for LRS Bianchi type-II spacetimes via Noether symmetries, Turanian J. Vol. 1, No. 3 (010304), 2025.