Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Discipline
- Institution
- Publication
- Publication Type
Articles 1 - 7 of 7
Full-Text Articles in Physical Sciences and Mathematics
Evaluation Of Black Holes In An Evolving Universe, John P. Naan
Evaluation Of Black Holes In An Evolving Universe, John P. Naan
Theses and Dissertations
There are various solutions to the Einstein field equations that represent different physical assumptions, but how to represent multiple black holes within an expanding universe remains an area of open interest. The first step to resolving this question involves evaluating spacetime models that contain a single black hole in an expanding universe. Here, we are primarily interested in understanding the energy distribution of black hole models by solving Einstein's equations using the associated spacetime metric and comparing the propagation of waves within the model against other known spacetime models. Specifically, we will evaluate the combined Schwarschild-de Sitter solution under a …
Equivalence: A Covariantly Constant Problem In General Relativity, Jaren Hobbs
Equivalence: A Covariantly Constant Problem In General Relativity, Jaren Hobbs
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
In studying the space-time structures described by Einstein’s theory of general relativity, it is often useful to identify particular properties referred to as geometrical invariants. These are attributes of the space-times which do not change regardless of the underlying coordinate systems used to study them. This project is part of a larger effort to catalogue space-times studied in general relativity. Specifically, computational software was used to identify structures known as covariantly constant vector fields.
The Equivalence Problem: Einstein-Maxwell Solutions, Rebecca Whitney
The Equivalence Problem: Einstein-Maxwell Solutions, Rebecca Whitney
Physics Capstone Projects
The “Equivalence Problem” is part of the Digital Einstein Project. The goal of this project is to create a digital and interactive library of all known solutions to the Einstein field equations in general relativity. The “Equivalence Problem” involves determining when two solutions are physically equivalent. This requires calculating physical and geometric features to characterize each solution independently of any coordinate system. One of the principal features used to characterize the solutions is the degree of symmetry or the isometry group of the space-time metric. We have focused on the solutions to the Einstein-Maxwell field equations and compared the isometry …
Rainich Geometrization Of Real Massless Scalar Fields, Dionisios Krongos
Rainich Geometrization Of Real Massless Scalar Fields, Dionisios Krongos
Physics Capstone Projects
Rainich geometrization is the process of eliminating the source from Einstein's field equations and thus expressing the equations solely with geometric quantities. This report briefly covers the theory, due to Kuchar, involved in the Rainich geometrization of a real massless scalar field with no cosmological constant. The theory contains the conditions which the Ricci tensor must satisfy such that the spacetime permits the scalar field and also explains the method used to reconstruct the field. Two procedures are written which automate this process and they are used extensively through the rest of the paper to both verify existing solutions, such …
Aspects Of General Relativity In 1+1 Dimensions, Richard D. Mellinger Jr
Aspects Of General Relativity In 1+1 Dimensions, Richard D. Mellinger Jr
Physics
What would be the properties of a universe with only one spatial dimension and one time dimension? General relativity in 1+1 dimensions is unique since the two curvature terms in the Einstein field equations cancel. This makes the Einstein field equations algebraic rather than differential equations. This special feature can make 1+1 dimensionality attractive as an instructional tool to simplify the mathematics that many beginners find opaque. We explore the implications and features of the Einstein field equations in 1+1 dimensions and find they provide a surprisingly rich and interesting model. We then study an alternate theory and its implications …
Generalized Emp And Nonlinear Schrodinger-Type Reformulations Of Some Scaler Field Cosmological Models, Jennie D'Ambroise
Generalized Emp And Nonlinear Schrodinger-Type Reformulations Of Some Scaler Field Cosmological Models, Jennie D'Ambroise
Open Access Dissertations
We show that Einstein’s gravitational field equations for the Friedmann- Robertson-Lemaître-Walker (FRLW) and for two conformal versions of the Bianchi I and Bianchi V perfect fluid scalar field cosmological models, can be equivalently reformulated in terms of a single equation of either generalized Ermakov-Milne- Pinney (EMP) or (non)linear Schrödinger (NLS) type. This work generalizes or presents an alternative to similar reformulations published by the authors who inspired this thesis: R. Hawkins, J. Lidsey, T. Christodoulakis, T. Grammenos, C. Helias, P. Kevrekidis, G. Papadopoulos and F.Williams. In particular we cast much of these authors’ works into a single framework via straightforward …
On The Linearization Stability Of The Conformally (Anti-) Self-Dual Einstein Equations, Charles G. Torre
On The Linearization Stability Of The Conformally (Anti-) Self-Dual Einstein Equations, Charles G. Torre
All Physics Faculty Publications
The Einstein equations with a cosmological constant, when restricted to Euclidean space‐times with anti‐self‐dual Weyl tensor, can be replaced by a quadratic condition on the curvature of an SU(2) (spin) connection. As has been shown elsewhere, when the cosmological constant is positive and the space‐time is compact, the moduli space of gauge‐inequivalent solutions to this equation is discrete, i.e., zero dimensional; when the cosmological constant is negative, the dimension of the moduli space is essentially controlled by the Atiyah–Singer index theorem provided the field equations are linearization stable. It is shown that linearization instability occurs whenever the unperturbed geometry possesses …