The central objective of this work is to present an analysis of the
asymptotic conformal Killing vectors in asymptotically-flat space-times
of general relativity. This problem has been examined by two different
methods; in Chapter 5 the asymptotic expansion technique originated by
Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes
which admit an asymptotically shear-free congruence of null
geodesics, and in Chapter 6 the conformal rescaling technique of Penrose
[54] is used both to support the findings of the previous chapter and to
set out a procedure for solution in the general case. It is pointed out
that Penrose's conformal technique is preferable to the use of asymptotic
expansion methods, since it can be established in a rigorous manner
without leading to the possible convergence difficulties associated with
asymptotic expansions.
Since the asymptotic conformal symmetry groups of asymptotically flat
space-times Are generalisations of the conformal group of Minkowski
space-time we devote Chapters 3 and 4 to a study of the flat space case so
that the results of later chapters may receive an interpretation in terms
of familiar concepts. These chapters fulfil a second, equally important,
role in establishing local isomorphisms between the Minkowski-space
conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been
used by Kastrup [61] to give a physical interpretation using space-time
gauge transformations. This appears as part of the survey of
interpretative work in Chapter 7. The SU(2,2) representation of the
conformal group has assumed a theoretical prominence in recent years.
through the work of Penrose [9-11] on twistors. In Chapter 4 we establish
contact with twistor ideas by showing that points in Minkowski space-time
correspond to certain complex skew-symmetric rank two tensors on the
SU(2,2) carrier space. These objects are, in Penrose's terminology [91,
simple skew-symmetric twistors of valence
[J.
A particularly interesting aspect of conformal objects in space-time is
explored in Chapter 8, where we extend the work of Geroch [16] on multipole
moments of the Laplace equation in 3-space to the consideration. of
Q tý =0 in Minkowski space-time. This development hinges upon the fact
that multipole moment fields are also conformal Killing tensors.
In the final chapter some elementary applications of the results of
Chapters 3 and 5 are made to cosmological models which have conformal
flatness or asymptotic conformal flatness. In the first class here we
have 'models of the Robertson-Walker type and in the second class we have
the asymptotically-Friedmann universes considered by Hawking [73]. / University of Bradford Research Studenship
| Identifer | oai:union.ndltd.org:BRADFORD/oai:bradscholars.brad.ac.uk:10454/3796 |
| Date | January 1976 |
| Creators | Griffin, G.K. |
| Contributors | Robinson, W.J. |
| Publisher | University of Bradford, Postgraduate School of Studies in Mathematics. |
| Source Sets | Bradford Scholars |
| Language | English |
| Detected Language | English |
| Type | Thesis, doctoral, PhD |
| Rights | <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http://creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. |
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