Current Search: Wilder, Shawn M. (x)


Title

Exploring a generalization of a definition for angular momentum on arbitrary Riemannian manifolds.

Creator

Wilder, Shawn M., Graduate College

Date Issued

20120330

PURL

http://purl.flvc.org/fcla/dt/3342458

Format

Document (PDF)


Title

Exploring the stability of an eigenvalue problem approximation technique used to define the angular momentum of almost spherical black holes.

Creator

Wilder, Shawn M., Beetle, Christopher, Graduate College

Date Issued

20110408

PURL

http://purl.flvc.org/fcla/dt/3164804

Subject Headings

Eigenvalues, Black holes (Astronomy), Deformations (Mechanics)

Format

Document (PDF)


Title

Approximate Isometries as an Eigenvalue Problem and Angular Momentum.

Creator

Wilder, Shawn M., Beetle, Christopher, Graduate College

Date Issued

20130412

PURL

http://purl.flvc.org/fcla/dt/3361373

Subject Headings

Black holes (Astronomy), Eigenvalues

Format

Document (PDF)


Title

General relativistic quasilocal angular momentum continuity and the stability of strongly elliptic eigenvalue problems.

Creator

Wilder, Shawn M., Beetle, Christopher, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Physics

Abstract/Description

In general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is welldefined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the...
Show moreIn general relativity, angular momentum of the gravitational field in some volume bounded by an axially symmetric sphere is welldefined as a boundary integral. The definition relies on the symmetry generating vector field, a Killing field, of the boundary. When no such symmetry exists, one defines angular momentum using an approximate Killing field. Contained in the literature are various approximations that capture certain properties of metric preserving vector fields. We explore the continuity of an angular momentum definition that employs an approximate Killing field that is an eigenvector of a particular secondorder differential operator. We find that the eigenvector varies continuously in Hilbert space under smooth perturbations of a smooth boundary geometry. Furthermore, we find that not only is the approximate Killing field continuous but that the eigenvalue problem which defines it is stable in the sense that all of its eigenvalues and eigenvectors are continuous in Hilbert space. We conclude that the stability follows because the eigenvalue problem is strongly elliptic. Additionally, we provide a practical introduction to the mathematical theory of strongly elliptic operators and generalize the above stability results for a large class of such operators.
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Date Issued

2014

PURL

http://purl.flvc.org/fau/fd/FA00004235

Subject Headings

Boundary element methods, Boundary value problems, Differential equations, Elliptic  Numerical solutions, Differential equations, Partial  Numerical solutions, Eigenvalues, Spectral theory (Mathematics)

Format

Document (PDF)