Abstract
Primordial black holes (PBHs) can form in the early universe, and there are several mass windows in which their abundance today may be large enough to comprise a significant part of the dark matter density. Additionally, numerical relativity (NR) allows one to investigate the formation processes of PBHs in the fully nonlinear strong-gravity regime.In this thesis, we will describe the use of NR methods to study PBH formation, motivated in particular by open questions about the nonspherical effects PBH formation in a matter-dominated early universe.
We demonstrate that superhorizon non-linear perturbations can collapse and form PBHs via the direct collapse or the accretion collapse mechanisms in a matter-dominated universe. The heaviest perturbations collapse via the direct collapse mechanism, while lighter perturbations trigger an accretion process that causes a rapid collapse of the ambient DM. From the hoop conjecture we propose an analytic criterion to determine whether a given perturbation will collapse via the direct or accretion mechanism and we compute the timescale of collapse. Independent of the formation mechanism, the PBH forms within an efold after collapse is initiated and with a small initial mass compared to the Hubble horizon, MBHH0 ∼ 10−2mP2l. Finally, we find that PBH formation is followed by extremely rapid growth MBH ∝ H−β with β ≫ 1, during which the PBH acquires most of its mass.
Furthermore, we study the formation of spinning primordial black holes during an early matter-dominated era. Using non-linear 3+1D general relativistic simulations, we compute the efficiency of mass and angular momentum transfer in the process – which we find to be O(10%). We show that subsequent evolution is important due to the seed PBH accreting non-rotating matter from the background, which decreases the dimensionless spin. Unless the matter era is short, we argue that the final dimensionless spins will be negligible.
Finally, we discuss the high computational cost of NR simulations and how these can be remedied in specific scenarios using dimensional reduction. We extend the modified cartoon method for the BSSN formalism by adding matter fields, specifically a real scalar field, and give explicit cartoon expressions for the evolution equations. Additionally, we give cartoon expressions for dimensional reduction of the CCTK method for finding NR initial conditions. We discuss the true vacuum bubble collision in the context of first-order phase transitions as a specific application of this work and show that our method provides continued stable numerical evolution of this process
| Date of Award | 1 Mar 2024 |
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| Original language | English |
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| Supervisor | Eugene Lim (Supervisor) |