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2nd Comment on “On the Klein–Gordon oscillator in topologically charged Ellis–Bronnikov type wormhole spacetime”

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Abstract

Attention is drawn to some circumstances that were not quite clearly described in the paper by Soares et al. (Eur Phys J Plus 136:966, 2021) and its previous comment by Amore and Fernandez (Eur Phys J Plus, 2024, this issue), in particular, that the Klein–Gordon field under consideration has a discrete spectrum of positive energy states, hard to be found analytically but approaching the spectrum of a usual quantum oscillator at high levels (\(n \gg 1\)). Corrections to the oscillator spectrum are here calculated in the WKB approximation.

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Data Availability Statement

No data associated in the manuscript.

Notes

  1. Here and henceforth an equation number of the form (1.N) refers to Eq. (N) from Ref.  [1], and that of the form (2.N) to Eq. (N) from Ref.  [2].

References

  1. A.R. Soares, L.L. Vitória, H. Aounallah, Eur. Phys. J. Plus 136, 966 (2021)

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  2. P. Amore, F.M. Fernández, Eur. Phys. J. Plus (2024) (to be published)

  3. H. Aounallah, A.R. Soares, R.L.L. Vitória, Eur. Phys. J. C 80, 447 (2020)

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Acknowledgements

This study was supported by RUDN Project FSSF-2023-0003. I would like to thank the anonymous referee for helpful remarks.

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Authors and Affiliations

  1. Center for Gravitation and Fundamental Metrology, VNIIMS, 46 Ozyornaya ul., Moscow, Russia, 119361

    K. A. Bronnikov

  2. Peoples’ Friendship University of Russia (RUDN University), ul. Miklukho-Maklaya 6., Moscow, Russia, 117198

    K. A. Bronnikov

  3. (Moscow Engineering Physics Institute), National Research Nuclear University “MEPhI”, Moscow, Russia

    K. A. Bronnikov

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  1. K. A. Bronnikov
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Correspondence to K. A. Bronnikov.

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Bronnikov, K.A. 2nd Comment on “On the Klein–Gordon oscillator in topologically charged Ellis–Bronnikov type wormhole spacetime”. Eur. Phys. J. Plus 139, 283 (2024). https://doi.org/10.1140/epjp/s13360-024-05076-4

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  • DOI: https://doi.org/10.1140/epjp/s13360-024-05076-4

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