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

## TL;DR

This paper introduces pseudo-spectral methods for simulating primordial black hole formation in a cosmological setting, confirming previous threshold estimates and analyzing mass scaling with improved numerical techniques.

## Contribution

First application of pseudo-spectral methods to spherically symmetric black hole formation in a FRW universe, providing independent verification and enhanced analysis capabilities.

## Key findings

- Confirmed previous threshold estimates for black hole formation.
- Estimated black hole masses with improved accuracy using excision and analytical methods.
- Validated the self-similar scaling law for black hole mass with about 15% accuracy.

## 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.