Spinors, embeddings and gravity.
University of Southampton, Department of Mathematics,
This thesis is concerned with the theory of spinors, embeddings and
everywhere invariance with applications to general relativity. The
approach is entirely geometric with particular emphasis on the use
of natural structures. A clear indication of the interaction between
the above topics is given; this Interaction then sheds light on
various aspects of general relativity theory.
The main ideas discussed are:- (i) Spinors, conformal structure
and the spacetime projective null bundle framework. (ii) Spaces of
embeddings. (ill) Embeddings and spin structure. (iv) Null embeddings
and the null limit (a technique for obtaining differential
equations on null hypersurfaces). (v) Quasi-local momentum.
(vi) The space of metrics, natural group actions and generalized
conformal structure. (vii) Everywhere invariance and the invariance
equation as a method for obtaining spacetime symmetries.
Three appendices are also provided:- These give comprehensive
summaries of the theories of principal bundles, conformal structure
and asymptotic simplicity.
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