test Browse by Author Names Browse by Titles of Works Browse by Subjects of Works Browse by Issue Dates of Works
       

Advanced Search
Home   
 
Browse   
Communities
& Collections
  
Issue Date   
Author   
Title   
Subject   
 
Sign on to:   
Receive email
updates
  
My Account
authorized users
  
Edit Profile   
 
Help   
About T-Space   

T-Space at The University of Toronto Libraries >
School of Graduate Studies - Theses >
Doctoral >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/32012

Title: Regge Calculus as a Numerical Approach to General Relativity
Authors: Khavari, Parandis
Advisor: Dyer, Charles C.
Department: Astronomy and Astrophysics
Keywords: Numerical Relativity
Regge Calculus
Issue Date: 17-Jan-2012
Abstract: A (3+1)-evolutionary method in the framework of Regge Calculus, known as "Parallelisable Implicit Evolutionary Scheme", is analysed and revised so that it accounts for causality. Furthermore, the ambiguities associated with the notion of time in this evolutionary scheme are addressed and a solution to resolving such ambiguities is presented. The revised algorithm is then numerically tested and shown to produce the desirable results and indeed to resolve a problem previously faced upon implementing this scheme. An important issue that has been overlooked in "Parallelisable Implicit Evolutionary Scheme" was the restrictions on the choice of edge lengths used to build the space-time lattice as it evolves in time. It is essential to know what inequalities must hold between the edges of a 4-dimensional simplex, used to construct a space-time, so that the geometry inside the simplex is Minkowskian. The only known inequality on the Minkowski plane is the "Reverse Triangle Inequality" which holds between the edges of a triangle constructed only from space-like edges. However, a triangle, on the Minkowski plane, can be built from a combination of time-like, space-like or null edges. Part of this thesis is concerned with deriving a number of inequalities that must hold between the edges of mixed triangles. Finally, the Raychaudhuri equation is considered from the point of view of Regge Calculus. The Raychaudhuri equation plays an important role in many areas of relativistic Physics and Astrophysics, most importantly in the proof of singularity theorems. An analogue to the Raychaudhuri equation in the framework of Regge Calculus is derived. Both (2+1)-dimensional and (3+1)-dimensional cases are considered and analogues for average expansion and shear scalar are found.
URI: http://hdl.handle.net/1807/32012
Appears in Collections:Doctoral

Files in This Item:

File Description SizeFormat
Khavari_Parandis_200911_PhD_thesis.pdf1.06 MBAdobe PDF
View/Open

Items in T-Space are protected by copyright, with all rights reserved, unless otherwise indicated.

uoft