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/1807/26247

Title: The Microcanonical Density of States and Causal Dynamical Triangulations
Authors: Thomson, Mitchell
Advisor: Dyer, Charles C.
Department: Physics
Keywords: General Relativity
Quantum Gravity
Issue Date: 17-Feb-2011
Abstract: Brown and York's gravitational microcanonical density of states is extended to general spacetime dimension and shown to be dependent upon features of the 4 dimensional gravitational action for its interpretation. Black hole entropy is calculated from the density of states path integral in general spacetime dimension, and the interpretation is shown to be likewise dependent upon the dimension of spacetime. The entropy of de Sitter and Rindler horizons are calculated using the black hole density of states and the notion of local horizon entropy density is shown to be supported. The applicability of the microcanonical ensemble to black hole mechanics is discussed at a fundamental level focussing on the absence of angular velocity as an external parameter in the gravitational Hamiltonian. The rotational ensemble and a new ensemble - the angular momentum ensemble - are introduced following Jaynes' information theory approach to statistical mechanics and proposed as more compelling candidates to calculate black hole entropy as a function of state. A program to calculate the density of states path integral non-perturbatively using causal dynamical triangulations is initiated. Regge calculus expressions for extrinsic curvature are extended to the case of Lorentzian hypersurfaces and used to derive Regge calculus expressions for quasilocal energy-momentum. The Regge version of the black hole density of states action is derived and specialised to the 3d and 4d spacetime constructions of causal dynamical triangulations. Finally, the recent suggestion that entropy is observer dependent is shown to be incompatible with the Tolman law for the equilibrium temperature in a gravitational field.
URI: http://hdl.handle.net/1807/26247
Appears in Collections:Doctoral

Files in This Item:

File Description SizeFormat
Thomson_Mitchell_R_201011_PhD_thesis.pdf607.77 kBAdobe PDF
View/Open

This item is licensed under a Creative Commons License
Creative Commons

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

uoft