High overtones of Dirac perturbations of a Schwarzschild black hole

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 ${\ensuremath{\omega}}_{n}$ is equidistant and equals to $\mathrm{I}\mathrm{m}({\ensuremath{\omega}}_{n+1})\ensuremath{-}\mathrm{I}\mathrm{m}({\ensuremath{\omega}}_{n})=i/8M$, $M$ being the black hole mass, which is twice less than that for fields of integer spin. At high overtones, the real part of ${\ensuremath{\omega}}_{n}$ 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.