Current Search: Newton-Raphson method. (x)
-
-
Title
-
Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-space.
-
Creator
-
Ray, Shannon, Miller, Warner A., Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics
-
Abstract/Description
-
One of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which,...
Show moreOne of the most fundamental problems in classical general relativity is the measure of e↵ective mass of a pure gravitational field. The principle of equivalence prohibits a purely local measure of this mass. This thesis critically examines the most recent quasi-local measure by Wang and Yau for a maximally rotating black hole spacetime. In particular, it examines a family of spacelike 2-surfaces with constant radii in Boyer-Lindquist coordinates. There exists a critical radius r* below which, the Wang and Yau quasi-local energy has yet to be explored. In this region, the results of this thesis indicate that the Wang and Yau quasi-local energy yields complex values and is essentially equivalent to the previously defined Brown and York quasi-local energy. However, an application of their quasi-local mass is suggested in a dynamical setting, which can potentially give new and meaningful measures. In supporting this thesis, the development of a novel adiabatic isometric mapping algorithm is included. Its purpose is to provide the isometric embedding of convex 2-surfaces with spherical topology into Euclidean 3-space necessary for completing the calculation of quasilocal energy in numerical relativity codes. The innovation of this algorithm is the guided adiabatic pull- back routine. This uses Ricci flow and Newtons method to give isometric embeddings of piecewise simplicial 2-manifolds, which allows the algorithm to provide accuracy of the edge lengths up to a user set tolerance.
Show less
-
Date Issued
-
2017
-
PURL
-
http://purl.flvc.org/fau/fd/FA00004865, http://purl.flvc.org/fau/fd/FA00004865
-
Subject Headings
-
Gravitational fields., General relativity (Physics), Newton-Raphson method., Ricci flow.
-
Format
-
Document (PDF)
