DECAY OF DIRAC FIELDS IN THE BACKGROUNDS OF DILATONIC BLACK HOLES

We find an exact solution to the Dirac equation in the background of the dilatonic black hole in 1+1 and 4+1 dimensions, and for them we calculate the corresponding quasinormal frequencies. In the two-dimensional case we find that for Weyl spinors the quasinormal modes' (QNM's) frequencies are pure imaginary and have negative sign for all modes, ensuring the stability of the (1+1)-dimensional dilatonic blackhole. We generalize results to the (4+1)-dimensional dilatonic black hole, where the metric is product of a two-dimensional a symptotically flat geometry and a three-sphere with a constant radius. Our conclusion is that the QNMs are pure imaginary, as in the (1+1)-dimensional case.