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arXiv · hep-th/0411055

High overtones of Dirac perturbations of a Schwarzschild black hole

K. H. C. Castello-Branco·R. A. Konoplya·A. Zhidenko
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Abstract

Using the Frobenius method, we find high overtones of the Dirac quasinormal spectrum for the Schwarzschild black hole. At high overtones, the spacing for imaginary part of $ω_{n}$ is equidistant and equals to $\Im{ω_{n+1}}-\Im{ω_{n}} =i/8M$, ($M$ is the black hole mass), which is twice less than that for fields of integer spin. At high overtones, the real part of $ω_{n}$ goes to zero. This supports the suggestion that the expected correspondence between quasinormal modes and Barbero-Immirzi parameter in Loop Quantum Gravity is just a numerical coincidence.

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K. H. C. Castello-Branco, R. A. Konoplya, A. Zhidenko. 2005-02-06. High overtones of Dirac perturbations of a Schwarzschild black hole. https://doi.org/10.1103/physrevd.71.047502

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