A study of numerical techniques for radiative problems in general relativity
department or school: Science, Faculty of
department or school: Physics and Astronomy, Department of
data provider: DSpace
degree campus: UBCV
creator: Choptuik, Matthew William
issued: 2010-07-30T18:30:07Z
issued: 1986
related degree: Doctor of Philosophy - PhD
degree grantor: University of British Columbia
description: There is continuing interest in the numerical solution of the field equations of general relativity. Many of the most interesting scenarios involve the generation and propagation of gravitational radiation—this thesis is an investigation of numerical techniques which should be useful for such problems. The study is based on a model system of a single massless scalar field coupled to the gravitational field, with the additional requirement of spherical symmetry. The 3+1 formalism for numerical relativity is used and attention is limited to finite difference techniques. As a preliminary step, the properties of some difference schemes are examined in the context of the wave equation in general coordinates. The accuracy, stability, convergence, dissipation, dispersion and efficiency of the schemes are discussed and three of the methods, which are all centred, second order approximations, are identified as being suitable for radiation problems in general relativity. Following work by Piran, the model problem is solved in three different coordinate systems using variations of the schemes devised for the wave equation. Various initial configurations of the scalar field are evolved, ranging from cases where there is a negligible amount of gravitational self-interaction to those where black holes are formed. Although some numerical difficulties remain with the latter calculations, the basic difference techniques developed for the treatment of the radiative degrees of freedom are found to be satisfactory. In the past it has been argued that there is a fundamental inconsistency in finite difference solutions of Einstein's equations which are generated by algorithms that do not continuously impose the constraint equations which arise from the coordinate freedom of general relativity. The deviations of freely evolved quantities from discrete versions of the constraint equations are supposedly of lower order (in the mesh spacing) than the underlying difference scheme. An argument…
aggregated CHO: https://circle.library.ubc.ca/rest/handle/2429/27043
note: A S t u d y of N u m e r i c a l T e c h n i q u e s for R a d i a t i v e P r o b l e m s G e n e r a l R e l a t i v i t y by M a t t h e w W i l l i a m C h o p t u i k B.Sc, Brandon University, 1980 M.Sc.,The University of British Columbia, 1982 A -Thesis S u b m i t t e d in P a r t i a l F u l f i l l m e n t of the R e q u i r e m e n t s for the Degree of D O C T O R O F P H I L O S O P H Y in T h e F a c u l t y of G r a d u a t e Studies D e p a r t m e n t of P h y s i c s We accept this thesis as conforming W the required standard T h e U n i v e r s i t y of B r i t i s h C o l u m b i a July 1986 © Matthew William Choptuik, 1986 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y o f B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head o f my department or by h i s o r her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of Physics The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 August 8, 1986 ii Abstract There is continuing interest in the numerical solution of the field equations of general relativity. Many of the most interesting scenarios involve the generation and propagation of gravitational radiation—this thesis is an investigation of numerical techniques which should be useful for such problems. The study is based on a model system of a single massless scalar field coupled to the gravitational field, with the additional requirement of spherical symmetry. The 3+1 formalism fo…
has type: Thesis/Dissertation
is shown at: 10.14288/1.0085044
language: eng
degree discipline: Physics
provider: Vancouver : University of British Columbia Library
publisher: University of British Columbia
rights: For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
scholar level: Graduate
type: Text
identifier URI: http://hdl.handle.net/2429/27043