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Title: Sectional curvature and plane waves in general relativity
Author: Hossack, Andrew D.
Awarding Body: University of Aberdeen
Current Institution: University of Aberdeen
Date of Award: 1992
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This thesis considers several problems in general relativity which involve the sectional curvature function σ. The causal structure defined by Lorentzian metrics on space-times makes the behaviour of σ more interesting in general relativity than in classical (positive-definite) geometry and comparisons between results in classical and Lorentzian geometry are made which illustrate this point. The thesis as a whole emphasises the geometrical rather than the physical aspects of the theory. There are three principal areas of study contained in this thesis: A theorem by J.L. Synge which relates sectional and Gaussian curvature along geodesics in classical geometry is introduced and generalised to Lorentzian geometry in a straight-forward manner. A result due to J. Beem and P. Parker concerning the existence of non-destructive null directions (along which gravitational tidal accelerations are bounded), in vacuum space-times is extended to arbitrary space-times in an elegant way. It is known that if a sectional curvature function σ is specified on a manifold then it is possible for two distinct, conformally-related generalised plane wave metrics to both give rise to σ. To investigate those symmetries of these space-times that might preserve σ, the concept of a sectional curvature preserving vector field on these plane waves is introduced and it is shown that these vector fields form a subalgebra of the conformal Lie algebra. A basis of this conformal algebra is then computed and used to establish conditions under which non-trivial sectional curvature preserving vector fields may exist. Other subsidiary results are also obtained as a consequence of these investigations.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Theoretical physics Physics Mathematics