Dirac Quasi-Normal Modes in Schwarzschild Black Hole Spacetimes

We evaluate both the massless and the massive Dirac quasi-normal mode frequencies in the Schwarzschild black hole spacetime using the WKB approximation. For the massless case, we find that, similar to those for the integral spin fields, the real parts of the frequencies increase with the angular momentum number $\kappa$, while the imaginary parts or the dampings increase with the mode number $n$ for fixed $\kappa$. For the massive case, the oscillation frequencies increase with the mass $m$ of the field, while the dampings decrease. Fields with higher masses will therefore decay more slowly.