## [1907.13065] Simulation of primordial black hole formation using pseudo-spectral methods

 Authors: Albert Escrivà Abstract: In this work we have used for the first time pseudo-spectral methods to perform numerical simulations of spherically symmetric black hole formations on a Friedman-Robertson-Walker universe. With these methods, the differential equations describing the gravitational collapse are partially solved algebraically. With our publicly available code we then independently check, and confirm, previous numerical estimations of the thresholds to form primordial black holes. By using an excision technique and analytical estimations of accretion rates, we were also able to estimate the black holes mass even in the case of large deviations from the threshold. There, we confirm, with an explicit example, that the estimation of the black hole mass via the self-similar scaling law is only accurate up to $O(15\%)$, for the largest allowed mass. [PDF]  [PS]  [BibTex]  [Bookmark]

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### [1907.13065] Simulation of primordial black hole formation using pseudo-spectral methods

This paper was commented on through Cosmo Comments. The following comments can also be viewed as annotations on the paper via Hypothesis.

The paper re-investigates the formation of primordial black holes (PBHs) from the collapse of large density perturbations. The author has produced a new code, which is made publicly available. The paper tests that the code produces the expected results regarding the formation threshold for PBHs and re-obtains the critical-scaling relationship which predicts the final PBH mass from the initial scale and amplitude of the perturbation which forms it. The paper does not present significant new results, but mostly just confirms previous findings.
A new result is that the paper studies the formation of PBHs from the largest allowed density perturbations – finding an error of O(15%) compared to the standard formula. However, to obtain this, the author makes use of an analytic expression to model the accretion of mass in the final stages and I am not sure of the accuracy of this. The critical-scaling formula is important for calculating the total PBH abundance and mass function. The abundance of the largest density perturbations is exponentially suppressed, even compared to the already exponentially small number of peaks large enough to form PBHs, i.e. this error is unlikely to be very important for such calculations. Could the author comment on the accuracy of the employed analytic expression to model mass accretion and the resulting uncertainties in the results?

Overall, the paper is well written and easy to follow. This would be a good starting point for anyone studying the formation, as it contains results previously spread out over multiple papers from years of study, and also makes the code available for other researchers to use.

[These comments were shared with us by a member of the cosmology community. They do not necessarily reflect the opinion of the Cosmo Comments team.]