virtual pair of particles is ripped apart by the electric field. In contrast to QED, the gravitational ‘charge’—the mass—is always positive; in this case, the tidal forces are thus responsible for the separation of the particle pair. But there is also another difference. The energy that is needed for the production of particles in a charged vacuum is taken out of the field energy. Since the energy of the gravitational field cannot be localised, the energy gain must be explained otherwise. One possibility is the existence of a horizon. Another possibility is the time dependence of the gravitational field.

We compute the particle production in a time-dependent gravitational field induced by an expanding mass shell. This is done at a semiclassical level. The gravitational field, which acts through curvature of space-time, is treated as a classical background field in which a quantum field propagates. We consider a massless scalar field. So it is quantum field theory in curved space that we need to apply.

Perhaps the best known result in this field is the thermal radiation emitted by a black hole. This effect, discovered by Hawking [@Haw], shows a deep connection between gravity, thermodynamics and quantum physics. Hawking’s result was 