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Title: Numerical general relativity and beyond : formation of relativistic axion stars, boosting and colliding oscillotons, and gravitational collapse in khronometric theory
Author: Widdicombe, James
ISNI:       0000 0004 9357 5849
Awarding Body: King's College London
Current Institution: King's College London (University of London)
Date of Award: 2020
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General Relativity (GR) is one of the wonders of the modern era. It beautifully predicts the nature of a strong gravitational field, and there are many exact analytical solutions that describe the world around us using GR. However there are many more scenarios that cannot be solved analytically, and furthermore, there are scenarios in which GR no longer makes sense. This thesis concerns itself with investigating these scenarios numerically using Numerical General Relativity (NR), as well as numerically probing what lies beyond GR, by studying a form of Lorentz-Violating gravity known as Khronometric Theory. The NR simulations were carried out using GRCHOMBO, which is a new open source code C++ 14, hybrid MPI/OpenMP code that utilises adaptive mesh refinement. Using GRCHOMBO, we study the formation of compact axion stars and black holes (BH) with aspherical initial conditions that could represent the final stages of axion dark matter structure formation. We show that the final states of such collapse closely follow the known relationship of initial mass and axion decay constant ƒa. We demonstrate with a toy model how this information can be used to scan a model density field to predict the number densities and masses of axion stars and BH. In addition to being detectable by the LIGO/VIRGO gravitational wave interferometer network for axion mass of 109 < ma < 1011 eV, we show using peak statistics that for ƒa < 0.2Mpl, there exists a "mass gap" between the masses of axion stars and BH formed from collapse. We investigate the physics of black hole formation from the head-on collisions of boosted equal mass oscillotons (OS) in NR, for both the cases where the OS have equal phases or are maximally o -phase (anti-phase). While unboosted OS collisions will form a BH as long as their initial compactness C ≡ GM/R is above a numerically determined critical value C > 0.035, we find that imparting a small initial boost counter-intuitively prevents the formation of black holes even if C > 0.035. If the boost is further increased, at very high boosts γ > 1/12C, BH formation occurs as predicted by the hoop conjecture, leading to a "stability band" where collisions result in either the OS "passing through" (equal phase) or "bouncing back" (antiphase), with a "critical point" occurring around C ≈ 0.07. We argue that the existence of this stability band can be explained by the competition between the free fall and the interaction timescales of the collision. Furthermore we provide an in-depth explanation of the construction of initial data for a pair of boosted OS as well as the modifications needed during evolution, and comment on the potential for further study. In the final part of this thesis, we investigate spherically symmetric gravitational collapse in Khronometric Theory. The system of equations is solved numerically using code written in C utilising the PETSc tool kit. We comment on a number of instabilities within the system and attempt to demonstrate why these exist. We attempt to regularise the system using a method from 1+1D spherically symmetric GR, however even after this regularisation the system does not appear to be stable. Finally, we comment on some ideas that could be used to stabilise the system both numerically and analytically, as well as discussing recent work by others in the field.
Supervisor: Lim, Eugene Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available