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Classical solutions to Bianchi type II spacetimes in f(R) theory of gravity

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Abstract

We consider the analytical solutions to the Bianchi type II universe in f(R) theory of gravity, a modified gravity theory. The Lagrangian and Hamiltonian are derived and the conformal vector fields of the space, which are Noether point symmetries of the Lagrangian, are presented. This spacetime is categorized into seven isometry classes. For each class, we establish the potential functionals V(t, x, y, z) and the first integrals associated with each Killing and homothetic vector field via Noether’s theorem. Subsequently, the Lagrangian of the Bianchi II spacetime is quantized yielding the Wheeler-DeWitt equation and we apply the zero-order invariants of the admitted Lie point symmetries to determine invariant solutions for the wave function of the universe. Lastly, we reduce the Hamiltonian system to acquire the exact classical solutions to the field equations for all seven classes.

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Acknowledgements

We acknowledge the financial support of the National Research Foundation of South Africa (SJ: 118047, UO:132750)

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  1. School of Mathematics, University of the Witwatersrand, Wits 2001, Johannesburg, South Africa

    U. Obaidullah & S. Jamal

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  1. U. Obaidullah
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  2. S. Jamal
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Correspondence to S. Jamal.

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Obaidullah, U., Jamal, S. Classical solutions to Bianchi type II spacetimes in f(R) theory of gravity. Indian J Phys 96, 3675–3688 (2022). https://doi.org/10.1007/s12648-021-02270-3

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  • DOI: https://doi.org/10.1007/s12648-021-02270-3

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