An analysis of the symmetries and conservation laws of some classes of nonlinear wave equations in curved spacetime geometry
Date
2013-08-08
Authors
Jamal, S
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Abstract
The (1+3) dimensional wave and Klein-Gordon equations are constructed using
the covariant d'Alembertian operator on several spacetimes of interest.
Equations on curved geometry inherit the nonlinearities of the geometry. These
equations display interesting properties in a number of ways. In particular, the
number of symmetries and therefore, the conservation laws reduce depending
on how curved the manifold is. We study the symmetry properties and
conservation laws of wave equations on Freidmann-Robertson-Walker, Milne,
Bianchi, and de Sitter universes. Symmetry structures are used to reduce the
number of unknown functions, and hence contribute to nding exact solutions
of the equations. As expected, properties of reduction procedures using symmetries,
variational structures and conservation laws are more involved than
on the well known
at (Minkowski) manifold.
Description
A thesis submitted to the Faculty of Science, University of the
Witwatersrand, in requirement for the degree Doctor of Philosophy,
Johannesburg, 2013.