UBC Theses and Dissertations
Numerical studies in gravitational collapse Akbarian Kaljahi, Arman
In the first part of this thesis, we solve the coupled Einstein-Vlasov system in spherical symmetry using direct numerical integration of the Vlasov equation in phase space. Focusing on the case of massless particles we study critical phenomena in the model, finding strong evidence for generic type I behaviour at the black hole threshold that parallels what has previously been observed in the massive sector. For differing families of initial data we find distinct critical solutions, so there is no universality of the critical configuration itself. However we find indications of at least a weak universality in the lifetime scaling exponent, which is yet to be understood. Additionally, we clarify the role that angular momentum plays in the critical behaviour in the massless case. The second part focuses on type II critical collapse. Using the critical collapse of a massless scalar field in spherical symmetry as a test case, we study a generalization of the BSSN formulation due to Brown that is suited for use with curvilinear coordinates. We adopt standard dynamical gauge choices, including 1+log slicing and a shift that is either zero or evolved by a Gamma-driver condition. With both choices of shift we are able to evolve sufficiently close to the black hole threshold to 1) unambiguously identify the discrete self-similarity of the critical solution, 2) determine an echoing exponent consistent with previous calculations, and 3) measure a mass scaling exponent, also in accord with prior computations. Our results can be viewed as an encouraging first step towards the use of hyperbolic formulations in more generic type II scenarios, including the as yet unresolved problem of critical collapse of axisymmetric gravitational waves. In the last part, we present simulations of nonlinear evolutions of pure gravity waves. We describe a new G-BSSN code in axial symmetry that is capable of evolving a pure vacuum content in a strong gravity regime for both Teukolsky and Brill initial data. We provide strong evidence for the accuracy of the numerical solver. Our results suggest that the G-BSSN is promising for type II critical phenomena studies.
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