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Quasi-local energy of rotating black hole spacetimes and isometric embeddings of 2-surfaces in Euclidean 3-space

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. / Includes bibliography. / Dissertation (Ph.D.)--Florida Atlantic University, 2017. / FAU Electronic Theses and Dissertations Collection

Identiferoai:union.ndltd.org:fau.edu/oai:fau.digital.flvc.org:fau_34583
ContributorsRay, Shannon (author), Miller, Warner A. (Thesis advisor), Florida Atlantic University (Degree grantor), Charles E. Schmidt College of Science, Department of Physics
PublisherFlorida Atlantic University
Source SetsFlorida Atlantic University
LanguageEnglish
Detected LanguageEnglish
TypeElectronic Thesis or Dissertation, Text
Format88 p., application/pdf
RightsCopyright © 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., http://rightsstatements.org/vocab/InC/1.0/

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