Dirac quasinormal modes of Schwarzschild black hole
Abstract
We investigate the Dirac quasinormal modes (QNMs) of a Schwarzschild black hole using continued fraction and Hill-determinant approaches. For large angular quantum number, we find that the fundamental quasinormal frequencies become evenly spaced and the spacing is given by ${\ensuremath{\omega}}_{\ensuremath{\lambda}+1}\ensuremath{-}{\ensuremath{\omega}}_{\ensuremath{\lambda}}=0.38490\ensuremath{-}0.00000i$, where $\ensuremath{\lambda}=\ifmmode\pm\else\textpm\fi{}(l+1/2)$ ($l$ is the angular quantum number). We show that the angular quantum number has a surprising effect of increasing real part but almost does not affect imaginary part of the quasinormal frequencies, especially for the lowest lying mode. We also find that the spacing for imaginary part of the quasinormal frequencies at high overtones is equidistant and equals to $\ensuremath{-}i/4M$, as it takes place for scalar, electromagnetic and gravitational perturbations.