  We study the magnitude of semiclassical gravity effects near the formation of
a black-hole horizon in spherically-symmetric spacetimes. As a probe for these
effects we use a quantised massless scalar field. Specifically, we calculate
two quantities derived from it: the renormalised stress-energy tensor (a
measure of how the field vacuum state affects the spacetime) and the effective
temperature function (a generalisation of Hawking temperature related to the
energy flux of the field vacuum). The subject of our study are spacetimes which
contain a spherical distribution of matter and an empty exterior Schwarzschild
region, separated by a surface which is moving in proximity to the
Schwarzschild radius $r_{\rm s}=2M$, with $M$ the total mass. In particular, we
analyse the consequences of three types of surface movement: an oscillation
just above $r_{\rm s}$, a monotonous approach towards $r_{\rm s}$ in infinite
time and a crossing of $r_{\rm s}$ at different velocities. For a collapsing
matter distribution which follows the expected dynamical evolution in general
relativity, we recover the standard picture of black-hole formation and its
tenuous semiclassical effects. In more general dynamical regimes, allowing
deviations from the standard classical evolution, we obtain a variety of
different effects: from the emission of Hawking-like radiation without the
formation of a horizon, to large values of the renormalised stress-energy
tensor, related to the Boulware vacuum divergence in static spacetimes.
