reproduced in several ways, but also other problems such as Unruh’s accelerated observer [@Unruh] or the gravitational analogue to the Casimir effect [@Casm] were studied.

In cosmological models, the production of particles plays a central role in explaining the origin of the structures observed in the Universe. During an epoch of cosmological inflation, quantum fluctuations of space-time and matter are amplified by the accelerated expansion of the Universe to become the seeds of large-scale structures [@infl].

All mentioned examples involve either a horizon, a boundary, or a singularity. To our knowledge, there exists no example in which particle production in an infinite space-time without horizon and without singularity has been calculated. The situation of an expanding mass shell represents such an example. We do not expect this work to have a direct astrophysical application, but the situation under study might be of interest when black holes evaporate. One could imagine that Hawking radiation is emitted from an evaporating black hole in a final burst, which we could then describe as a thin shell, carrying a mass somewhat larger than the Planck mass. If the emitted radiation consists of massive particles, this mass shell moves at a speed slightly below the 