2 research outputs found
Probability of primordial black hole formation and its dependence on the radial profile of initial configurations
In this paper we derive the probability of the radial profiles of spherically
symmetric inhomogeneities in order to provide an improved estimation of the
number density of primordial black holes (PBHs). We demonstrate that the
probability of PBH formation depends sensitively on the radial profile of the
initial configuration. We do this by characterising this profile with two
parameters chosen heuristically: the amplitude of the inhomogeneity and the
second radial derivative, both evaluated at the centre of the configuration. We
calculate the joint probability of initial cosmological inhomogeneities as a
function of these two parameters and then find a correspondence between these
parameters and those used in numerical computations of PBH formation. Finally,
we extend our heuristic study to evaluate the probability of PBH formation
taking into account for the first time the radial profile of curvature
inhomogeneities.Comment: Version 2 with corrections from referees included, changes mostly
improve the presentatio
Primordial black hole formation in the radiative era: investigation of the critical nature of the collapse
Following on after two previous papers discussing the formation of primordial
black holes in the early universe, we present here results from an in-depth
investigation of the extent to which primordial black hole formation in the
radiative era can be considered as an example of the critical collapse
phenomenon. We focus on initial supra-horizon-scale perturbations of a type
which could have come from inflation, with only a growing component and no
decaying component. In order to study perturbations with amplitudes extremely
close to the supposed critical limit, we have modified our previous computer
code with the introduction of an adaptive mesh refinement scheme. This has
allowed us to follow black hole formation from perturbations whose amplitudes
are up to eight orders of magnitude closer to the threshold than we could do
before. We find that scaling-law behaviour continues down to the smallest black
hole masses that we are able to follow and we see no evidence of shock
production such as has been reported in some previous studies and which led
there to a breaking of the scaling-law behaviour at small black-hole masses. We
attribute this difference to the different initial conditions used. In addition
to the scaling law, we also present other features of the results which are
characteristic of critical collapse in this context.Comment: 21 pages, 7 figures, the present version is updated with some changes
and two new appendix. Accepted for pubblication in Classical and Quantum
Gravit