Hawking radiation of massive fields in 2D

Abstract

We extend the classic results of the paper [P. C. W. Davies, S. A. Fulling, and W. G. Unruh, Phys. Rev. D 13, 2720 (1976).] “Energy-momentum tensor near an evaporating black hole” by considering a massive scalar field in a two dimensions in the presence of a thin shell collapse. We show that outside the shell the WKB approximation is valid for any value of $r$ if $m{r}_g\gg 1$, where $m$ is the mass of the field, and $r_g$ is the Schwarzschild radius. Thus, we use semiclassical modes to calculate the flux in the vicinity of the shell, and at spatial infinity, $r\to +\infty$ at the final stage of the collapse, $t\to +\infty$ with the use of the covariant point-splitting regularization. We get that near the shell and at the spatial infinity the radiation is thermal with Hawking temperature. We obtain the negative flux $T_{vv}$ in the vicinity of the shell, which is similar to the classic result in the massless case.