ETD Collection

Permanent URI for this collectionhttps://wiredspace.wits.ac.za/handle/10539/104


Please note: Digitised content is made available at the best possible quality range, taking into consideration file size and the condition of the original item. These restrictions may sometimes affect the quality of the final published item. For queries regarding content of ETD collection please contact IR specialists by email : IR specialists or Tel : 011 717 4652 / 1954

Follow the link below for important information about Electronic Theses and Dissertations (ETD)

Library Guide about ETD

Browse

Filters

20241

Settings

Author: search.filters.author.Obaidullah, UsaamahSubject: search.filters.subject.Symmetry analysis

Search Results

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Symmetry analysis of geometries in general relativity and mathematical models in quantitative finance
    (2024) Obaidullah, Usaamah
    This thesis may be divided into two themes. The first, consists of a mathematical analysis of selected models in cosmology, while the second, is in the field of quantitative finance. The pp-wave spacetime, Bianchi I spacetime, and the Bianchi II spacetime are the three universes that we examine. The latter two are studied in the framework of f(R) theory of gravity, a plausible substitute for general relativity and a solution to the dark energy problem. We apply the Killing and homothetic vector fields to divide the spacetimes into classes or categories. Subsequently, potential functions are established using the geometry of the point symmetries of the space, while Noether’s theorem provides the first integrals connected to each isometry. We take advantage of the geometric fact that the homothetic algebra of spacetimes yields the Noether point symmetries of geodesic Lagrangians. For the Bianchi spacetimes, the Wheeler-DeWitt equations are derived by the quantisation of the spacetime Lagrangians, and from the Lie point symmetries it admits, we sequentially find invariant solutions to solve for the universe’s wave function. Finally, exact solutions to the field equations are also found. The research comprising of the second theme, investigates two nonlinear partial differential equations used in derivative pricing for financial markets. The point symmetries, invariant solutions, and conversation laws of these equations are found. In our analysis, we vary certain variables that change the nonlinearity of the models and thus give us unique symmetries and solutions. With various parameter settings, graphical solutions are investigated.