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On Some Aspects of the Holographic Pole-Skipping Phenomenon

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Abstract

We study various aspects of the recently discovered holographic pole-skipping phenomenon. We consider pole-skipping in the holographic dual of rotating black holes for the scalar field and metric perturbations. We determine the Lyapunov exponent and butterfly velocity from holographic gravitational pole-skipping points. We also study the first pole-skipping point for the scalar field in various backgrounds including rotating and charged black holes, and we take into account the interaction with the background electromagnetic field.

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Notes

  1. Note that \(\Lambda\) is related to the so-called AdS radius \(\ell\) as \(\Lambda=-1/\ell^2\). We take \(\ell=1\) in all calculations.

  2. Moreover, this equation must vanish identically on-shell for all \(r\), i.e., for the choice of \(f(r)\), \(G(r)\), and \(g(r)\) in the form (2.5).

  3. One can show that only this choice is relevant to the nondiagonal perturbation under consideration (see [8]).

  4. Again we assume the ansatz in the form of an infalling wave (see (3.4) below).

  5. With \(G(r)\) and \(f(r)\) vanishing at \(r_+\).

  6. Again we assume that on the horizon \(f(r_+)=0\) and \(A(r_+)=0\).

References

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Funding

This work is supported by the Russian Science Foundation under grant 20-12-00200.

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Authors and Affiliations

  1. Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    Dmitry S. Ageev

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  1. Dmitry S. Ageev
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Correspondence to Dmitry S. Ageev.

Additional information

Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Vol. 313, pp. 7–13 https://doi.org/10.4213/tm4182.

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Ageev, D.S. On Some Aspects of the Holographic Pole-Skipping Phenomenon. Proc. Steklov Inst. Math. 313, 1–7 (2021). https://doi.org/10.1134/S0081543821020012

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  • DOI: https://doi.org/10.1134/S0081543821020012

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