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Stability of circular geodesics in equatorial plane of Kerr spacetime

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Abstract

We analyze the stability of circular geodesics for timelike as well as null geodesics of the Kerr BH spacetime with rotation parameter on the equatorial plane by Lyapunov stability analysis. Also, we verify the results of stability by presenting the phase portrait for both timelike and null geodesics. Further, by reviewing the Kosambi–Cartan–Chern (KCC) theory, we analyze the Jacobi stability for Kerr spacetime and present a comparative study of the methods used for stability analysis of geodesics.

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Acknowledgements

P.S. would like to thank University Grants Commission \(\left( UGC\right) \), New Delhi, India for providing the financial support as a Junior Research Fellow through UGC-Ref.No. 1060/CSIR-UGC NET-JUNE2018. H.N. thankfully acknowledges the financial support provided by Science and Engineering Research Board(SERB), India through grant no. EMR/2017/000339. The authors also acknowledge the facilities available at ICARD, Gurukula Kangri (Deemed to be University) Haridwar those were used during the course of this work.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Gurukula Kangri (Deemed to be University), Haridwar, Uttarakhand, 249 404, India

    Pradeep Singh & Nidhi Handa

  2. Department of Physics, Gurukula Kangri (Deemed to be University), Haridwar, Uttarakhand, 249 404, India

    Hemwati Nandan & Shobhit Giri

  3. Center for Space Research, North-West University, Mahikeng, 2745, South Africa

    Hemwati Nandan

  4. Department of Applied Science, Faculty of Engineering and Technology, Gurukula Kangri (Deemed to be University), Haridwar, Uttarakhand, 249 404, India

    Lokesh Kumar Joshi

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  1. Pradeep Singh
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  2. Hemwati Nandan
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  4. Nidhi Handa
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  5. Shobhit Giri
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Correspondence to Hemwati Nandan.

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Singh, P., Nandan, H., Joshi, L.K. et al. Stability of circular geodesics in equatorial plane of Kerr spacetime. Eur. Phys. J. Plus 137, 263 (2022). https://doi.org/10.1140/epjp/s13360-022-02477-1

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