Ilia Musco, John C. Miller
Following on after three previous papers discussing the formation of
primordial black holes during the radiation-dominated era of the early
universe, we present here a further investigation of the critical nature of the
collapse. In particular, we focus on the long-lived intermediate state, which
appears in collapses of perturbations close to the critical limit, and examine
the extent to which this follows a similarity solution, as seen for critical
collapse under more idealized circumstances (rather than within the context of
an expanding universe, as studied here). We find that a similarity solution is
indeed realised, to good approximation, for a region contained within the past
light-cone of the forming black hole (and eventual singularity). The
self-similarity is not exact, however, and this is explained by the presence
within the light-cone of some outer matter still coupled to the expanding
universe, which does not participate in the self-similarity. Our main interest,
from a cosmological point of view, is in a radiative fluid with equation of
state parameter $w=1/3$ (when the pressure $p$ and energy density $e$ are taken
to be related by $p = we$). Other values of $w$, in the range $0 - 1$, have
also been considered in the literature on critical collapse and we have looked
at some of these too, within the context of our calculations, with the aim of
gaining further insight into our main case of interest. As expected, we find
that the features of scaling-law behaviour, intermediate state and similarity
solution are preserved in all of the cases studied but with some interesting
variations in the details. As in our previous work, we have started our
simulations with initial supra-horizon scale perturbations of a type which
could have come from inflation.
View original:
http://arxiv.org/abs/1201.2379
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