Late-time behavior of massive Dirac fields in a Schwarzschild background

The late-time tail behavior of massive Dirac fields is investigated in the Schwarzschild black-hole geometry and the result is compared with that of the massive scalar fields. It is shown that in the intermediate late times there are three kinds of differences between the massive Dirac and scalar fields: (i) The asymptotic behavior of massive Dirac fields is dominated by a decaying tail without any oscillation, but the massive scalar field by a oscillatory inverse power-law decaying tail; (ii) the dumping exponent for the massive Dirac field depends not only on the multiple number of the wave mode but also on the mass of the Dirac field, while that for the massive scalar field depends on the multiple number only; and (iii) the decay of the massive Dirac field is slower than that of the massive scalar field.