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.
