Skip to main content
SpringerLink
Log in

On Kerr black hole deformations admitting a Carter constant and an invariant criterion for the separability of the wave equation

  • Research Article
  • Published:
General Relativity and Gravitation Aims and scope Submit manuscript

Abstract

In a previous work of ours, the most general family of Kerr deformations—admitting a Carter constant—has been presented. This time a simple, necessary and sufficient condition in order for the aforementioned family to have a separable Klein-Gordon equation is exhibited. In addition, we provide a solid theoretical foundation that the maximum number of free to be chosen radial functions is three.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

Notes

  1. In [17] a misunderstanding of the results published in [1] is apparent. More specifically, it is mentioned that according to [1] the Kerr-Sen metric [18] cannot be mapped to the Johannsen metric [2] and that in [17] it is proven to be possible. The correct statement in [1] is that the Killing tensor of the Kerr-Sen metric, which is of Petrov type I, is not induced by a Yano tensor—and thus, it is somehow more general than the rest of the examples, which are of the Petrov type D. Never the less the Johannsen metric is—in priciple—of Petrov type I as well and contains much freedom so that the Kerr-Sen metric can be considered as a member of the this family.

  2. The exact form of g is quite extended to be written here.

References

  1. Papadopoulos, G.O., Kokkotas, K.D.: Class. Quant. Grav. 35, 185014 (2018)

    Article  ADS  Google Scholar 

  2. Johannsen, T.: Phys. Rev. D 88, 044002 (2013)

    Article  ADS  Google Scholar 

  3. Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.X., et al.: Phys. Rev. Lett. 116, 061102 (2016a)

    Article  ADS  MathSciNet  Google Scholar 

  4. Abbott, B.P., Abbott, R., Abbott, T.D., Abernathy, M.R., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.X., et al.: Phys. Rev. Lett. 116, 221101 (2016b)

    Article  ADS  Google Scholar 

  5. Event Horizon Telescope Collaboration, K. Akiyama, A. Alberdi, W. Alef, K. Asada, R. Azulay, A.-K. Baczko, D. Ball, M. Baloković, J. Barrett, et al., ApJ 875, L1 (2019)

  6. Medeiros, L., Psaltis, D., Özel, F.: ApJ 896, 7 (2020)

    Article  ADS  Google Scholar 

  7. Barack, L., Cardoso, V., Nissanke, S., Sotiriou, T.P., Askar, A., Belczynski, C., Bertone, G., Bon, E., Blas, D., Brito, R., et al.: Class. Quant. Grav. 36, 143001 (2019)

    Article  ADS  Google Scholar 

  8. E. Barausse, E. Berti, T. Hertog, S. A. Hughes, P. Jetzer, P. Pani, T. P. Sotiriou, N. Tamanini, H. Witek, K. Yagi, et al., arXiv e-prints arXiv:2001.09793 (2020)

  9. Okounkova, M., Stein, L.C., Moxon, J., Scheel, M.A., Teukolsky, S.A.: Phys. Rev. D 101, 104016 (2020)

    Article  ADS  Google Scholar 

  10. Carter, B.: Phys. Rev. 174, 1559 (1968)

    Article  ADS  Google Scholar 

  11. Ryan, F.D.: Phys. Rev. D 52, 5707 (1995)

    Article  ADS  Google Scholar 

  12. Glampedakis, K., Babak, S.: Class. Quant. Grav. 23, 4167 (2006)

    Article  ADS  Google Scholar 

  13. Collins, N.A., Hughes, S.A.: Phys. Rev. D 69, 124022 (2004)

    Article  ADS  MathSciNet  Google Scholar 

  14. Johannsen, T., Psaltis, D.: Phys. Rev. D 83, 124015 (2011)

    Article  ADS  Google Scholar 

  15. Konoplya, R.A., Stuchlík, Z., Zhidenko, A.: Phys. Rev. D 97, 084044 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  16. Shaikh, R.: Phys. Rev. D 100, 024028 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  17. Carson, Z., Yagi, K.: Phys. Rev. D 101, 084030 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  18. Sen, A.: Phys. Rev. Lett. 69, 1006 (1992)

    Article  ADS  MathSciNet  Google Scholar 

  19. Suvorov, A.G.: Phys. Rev. D 99, 124026 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  20. Brill, D.R., Chrzanowski, P.L., Pereira, C.M., Fackerell, E.D., Ipser, J.R.: Phys. Rev. D 5, 1913 (1972)

    Article  ADS  MathSciNet  Google Scholar 

  21. Teukolsky, S.A.: Phys. Rev. Lett. 29, 1114 (1972)

    Article  ADS  Google Scholar 

  22. Chen, C.-Y., Chen, P.: Phys. Rev. D 100, 104054 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  23. Landau, L.D., Lifshitz, E.M.: The classical theory of fields. Pergamon Press (1975)

Download references

Acknowledgements

The authors are grateful to K. Destounis, S. Nampalliwar, K. Yagi and A. G. Suvorov for useful discussions. This work was supported by the DAAD program “Hochschulpartnerschaften mit Griechenland 2016” (Projekt 57340132). Networking support by the COST Action CA16104 is also gratefully acknowledged

Author information

Authors and Affiliations

  1. Department of Physics, National and Kapodistrian University of Athens, Panepistimioupolis, Athens, GR 157-71, Greece

    Georgios O. Papadopoulos

  2. Theoretical Astrophysics, IAAT, Eberhard Karls University of Tübingen, 72076, Tubingen, Germany

    Kostas D. Kokkotas

Authors
  1. Georgios O. Papadopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kostas D. Kokkotas
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Georgios O. Papadopoulos.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Papadopoulos, G.O., Kokkotas, K.D. On Kerr black hole deformations admitting a Carter constant and an invariant criterion for the separability of the wave equation. Gen Relativ Gravit 53, 21 (2021). https://doi.org/10.1007/s10714-021-02795-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10714-021-02795-2

Keywords

Mathematics Subject Classification

Search

Navigation