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Among the different methods to derive particle creation, finding the quantumstress tensor expectation value gives a covariant quantity which can be usedfor examining the back-reaction issue. However this tensor also includes vacuumpolarization in a way that depends on the vacuum chosen. Here we reviewdifferent aspects of particle creation by looking at energy conservation and atthe quantum stress tensor. It will be shown that in the case of generalspherically symmetric black holes that have a \emph{dynamical horizon}, asoccurs in a cosmological context, one cannot have pair creation on the horizonbecause this violates energy conservation. This confirms the results obtainedin other ways in a previous paper [25]. Looking at the expectation value of thequantum stress tensor with three different definitions of the vacuum state, westudy the nature of particle creation and vacuum polarization in black hole andcosmological models, and the associated stress energy tensors. We show that thethermal temperature that is calculated from the particle flux given by thequantum stress tensor is compatible with the temperature determined by theaffine null parameter approach. Finally, it will be shown that in thespherically symmetric dynamic case, we can neglect the backscattering term andonly consider the s-waves term near the future apparent horizon.

Particle creation from the quantum stress tensor