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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