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

TL;DR

This paper analyzes the late-time decay behavior of massive Dirac fields around Schwarzschild black holes, highlighting differences from scalar fields in decay patterns, oscillations, and dependence on mass and mode number.

Contribution

It provides a detailed comparison of the late-time tails of massive Dirac and scalar fields in Schwarzschild spacetime, revealing unique decay characteristics of Dirac fields.

Findings

Dirac fields decay without oscillations, unlike scalar fields.

The decay rate of Dirac fields depends on mass and mode number.

Dirac fields decay more slowly than scalar fields.

Abstract

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 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.