2005/08/02 by Nicolae Tarfulea, Tarfulea, Nicolae
Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.48550/arxiv.gr-qc/0508014
108 pages, 4 figures, Ph.D. thesis (University of Minnesota)
arxiv created 2005/08/02 · openalex publication_date 2005/08/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
Einstein's system of equations in the ADM decomposition involves two subsystems of equations: evolution equations and constraint equations. For numerical relativity, one typically solves the constraint equations only on the initial time slice, and then uses the evolution equations to advance the solution in time. Our interest is in the case when the spatial domain is bounded and appropriate boundary conditions are imposed. A key difficulty, which we address in this thesis, is what boundary conditions to place at the artificial boundary that lead to long time stable numerical solutions. We develop an effective technique for finding well-posed constraint preserving boundary conditions for constrained first order symmetric hyperbolic systems. By using this technique, we study the preservation of constraints by some first order symmetric hyperbolic formulations of Einstein's equations derived from the ADM decomposition linearized around Minkowski spacetime with arbitrary lapse and shift perturbations, and the closely related question of their equivalence with the linearized ADM system. Our main result is the finding of well-posed maximal nonnegative constraint preserving boundary conditions for each of the first order symmetric hyperbolic formulations under investigation, for which the unique solution of the corresponding initial boundary value problem provides a solution to the linearized ADM system on polyhedral domains.