You are here
Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-space
| Title: | Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-space. |
 161 views 49 downloads |
|---|---|---|
| Name(s): |
Ray, Shannon, author Miller, Warner A., Thesis advisor Florida Atlantic University, Degree grantor Charles E. Schmidt College of Science Department of Physics |
|
| Type of Resource: | text | |
| Genre: | Electronic Thesis Or Dissertation | |
| Date Created: | 2017 | |
| Date Issued: | 2017 | |
| Publisher: | Florida Atlantic University | |
| Place of Publication: | Boca Raton, Fla. | |
| Physical Form: | application/pdf | |
| Extent: | 88 p. | |
| Language(s): | English | |
| Summary: | 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, 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. | |
| Identifier: | FA00004865 (IID) | |
| Degree granted: | Dissertation (Ph.D.)--Florida Atlantic University, 2017. | |
| Collection: | FAU Electronic Theses and Dissertations Collection | |
| Note(s): | Includes bibliography. | |
| Subject(s): |
Gravitational fields. General relativity (Physics) Newton-Raphson method. Ricci flow. |
|
| Held by: | Florida Atlantic University Libraries | |
| Sublocation: | Digital Library | |
| Links: | http://purl.flvc.org/fau/fd/FA00004865 | |
| Persistent Link to This Record: | http://purl.flvc.org/fau/fd/FA00004865 | |
| Use and Reproduction: | Copyright © is held by the author, with permission granted to Florida Atlantic University to digitize, archive and distribute this item for non-profit research and educational purposes. Any reuse of this item in excess of fair use or other copyright exemptions requires permission of the copyright holder. | |
| Use and Reproduction: | http://rightsstatements.org/vocab/InC/1.0/ | |
| Host Institution: | FAU | |
| Is Part of Series: | Florida Atlantic University Digital Library Collections. |
