  In this paper, we present a careful study on the impact of neutrino
pair-production on core-collapse supernovae via spherically-symmetric,
general-relativistic simulations of two different massive star progenitors with
energy-dependent neutrino transport. We explore the impact and consequences of
both the underlying microphysics and the implementation in the radiation
transport algorithms on the supernova evolution, neutrino signal properties,
and the explosion dynamics. We consider the two dominant neutrino
pair-production processes found in supernovae, electron-positron annihilation
as well as nucleon-nucleon bremsstrahlung in combination with both a simplified
and a complete treatment of the processes in the radiation transport
algorithms. We find that the use of the simplified prescription quantitatively
impacts the neutrino signal at the 10\% level and potentially the supernova
dynamics, as we show for the case of a 9.6M$_\odot$ progenitor. We also show
that the choice of nucleon-nucleon bremsstrahlung interaction can also have a
quantitative impact on the neutrino signal. A self-consistent treatment with
state-of-the-art microphysics is suggested for precision simulations of core
collapse, however the simplified treatment explored here is both
computationally less demanding and results in a qualitatively similar
evolution.
