Computations of primordial black hole formation

TL;DR

This paper presents numerical simulations of primordial black hole formation during the radiation era, analyzing perturbation evolution, thresholds, and effects of vacuum energy using relativistic models.

Contribution

It provides new insights into the threshold amplitudes for black hole formation and the impact of vacuum energy on scaling laws, extending previous studies with detailed numerical analysis.

Findings

Confirmed scaling-laws for super-critical perturbations

Lowered threshold amplitude for black hole formation with purely growing modes

Quantified effects of vacuum energy on thresholds and scaling slopes

Abstract

Results are presented from general relativistic numerical computations of primordial black-hole formation during the radiation-dominated era of the universe. Growing-mode perturbations are specified within the linear regime and their subsequent evolution is followed as they become nonlinear. We use a spherically symmetric Lagrangian code and study both super-critical perturbations, which go on to produce black holes, and sub-critical perturbations, for which the overdensity eventually disperses into the background medium. For super-critical perturbations, we confirm the results of previous work concerning scaling-laws but note that the threshold amplitude for a perturbation to lead to black-hole formation is substantially reduced when the initial conditions are taken to represent purely growing modes. For sub-critical cases, where an initial collapse is followed by a subsequent re-expansion, strong compressions and rarefactions are seen for perturbation amplitudes near to the threshold. We have also investigated the effect of including a significant component of vacuum energy and have calculated the resulting changes in the threshold and in the slope of the scaling law.