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An alternative to the Teukolsky equation

Abstract

We conjecture a new ordinary differential equation exactly isospectral to the radial component of the homogeneous Teukolsky equation. We find this novel relation by a hidden symmetry implied from a four-dimensional \(\mathcal {N}=2\) supersymmetric quantum chromodynamics. Our proposal is powerful both in analytical and in numerical studies. As an application, we derive high-order perturbative series of quasinormal mode frequencies in the slowly rotating limit. We also test our result numerically by comparing it with a known technique.

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Fig. 1
Fig. 2

Notes

  1. 1.

    It seems that the Eq. (1) can be derived by a highly non-trivial integral transformation in [8, 9]. We are grateful to Masato Nozawa for pointing out this fact with his great insight. We stress that the authors in [8, 9] did not mention the particularly useful Eq. (1).

  2. 2.

    We thank Hajime Nagoya for pointing out this fact.

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Acknowledgements

We thank Gleb Aminov, Alba Grassi, Katsushi Ito, Masashi Kimura, Hajime Nagoya and Masato Nozawa for valuable discussions. This work is supported by JSPS KAKENHI Grant Number JP18K03657.

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Correspondence to Yasuyuki Hatsuda.

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Hatsuda, Y. An alternative to the Teukolsky equation. Gen Relativ Gravit 53, 93 (2021). https://doi.org/10.1007/s10714-021-02866-4

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Keywords

  • Black hole perturbation theory
  • Quasinormal modes of balck holes
  • Supersymmetric gauge theories