  Among the different methods to derive particle creation, finding the quantum
stress tensor expectation value gives a covariant quantity which can be used
for examining the back-reaction issue. However this tensor also includes vacuum
polarization in a way that depends on the vacuum chosen. Here we review
different aspects of particle creation by looking at energy conservation and at
the quantum stress tensor. It will be shown that in the case of general
spherically symmetric black holes that have a \emph{dynamical horizon}, as
occurs in a cosmological context, one cannot have pair creation on the horizon
because this violates energy conservation. This confirms the results obtained
in other ways in a previous paper [25]. Looking at the expectation value of the
quantum stress tensor with three different definitions of the vacuum state, we
study the nature of particle creation and vacuum polarization in black hole and
cosmological models, and the associated stress energy tensors. We show that the
thermal temperature that is calculated from the particle flux given by the
quantum stress tensor is compatible with the temperature determined by the
affine null parameter approach. Finally, it will be shown that in the
spherically symmetric dynamic case, we can neglect the backscattering term and
only consider the s-waves term near the future apparent horizon.
