---
abstract: 'We compute the production of particles from the gravitational field of an expanding mass shell. Contrary to the situation of Hawking radiation and the production of cosmological perturbations during cosmological inflation, the example of an expanding mass shell has no horizon and no singularity. We apply the method of ‘ray-tracing’, first introduced by Hawking, and calculate the energy spectrum of the produced particles. The result depends on three parameters: the expansion velocity of the mass shell, its radius, and its mass. Contrary to the situation of a collapsing mass shell, the energy spectrum is non-thermal. Invoking time reversal we reproduce Hawking’s thermal spectrum in a certain limit.'
address:
- '${}^\dag$Institut für Theoretische Physik, J.W.Goethe-Universität, Robert-Mayer-Str. 8–10, 60054 Frankfurt am Main, Germany'
- '${}^\ddag$Institut für Theoretische Physik, Technische Universität Wien, Wiedner Hauptstr. 8–10, 1040 Vienna, Austria'
- '${}^*$Theory Divison, CERN, 1211 Geneva 23, Switzerland'
author:
- 'Sabine Hossenfelder,$^\dag$ Dominik J. Schwarz,$^{\ddag *}$ Walter Greiner$^\dag$'
title: 'Particle production in time-dependent gravitational fields: the expanding mass shell'
---

CERN-2002-286\

Introduction
============

Gradients in a gravitational field may cause the production of particles out of the vacuum; this is similar to the situation in quantum electrodynamics (QED). In the latter case a 