{"id":{"repo_id":"bradford","oai_identifier":"oai:bradscholars.brad.ac.uk:10454/3796"},"canonical_url":"https://search.dev.ndltd.org/etd/bradford/oai:bradscholars.brad.ac.uk:10454/3796","repository":{"repo_id":"bradford","name":"University of Bradford","base_url":"https://bradscholars.brad.ac.uk/oai/request"},"display":{"title":"Conformal symmetries in special and general relativity.The derivation and interpretation of conformal symmetries and asymptotic conformal symmetries in Minkowski space-time and in some space-times of general relativity.","abstract":"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].","abstract_html":"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].","abstract_has_math":false,"creators":["Griffin, G.K."],"institution":"University of Bradford","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":["Robinson, W.J."],"committee_chairs":[],"committee_members":[],"year":2009,"date_issued":"2009-10-28T16:29:40Z","date_published":"2009-10-28T16:29:40Z","updated_at":"2026-07-24T01:14:44Z","subjects":["Asymptotic conformal Killing vectors","Asymptotically-flat space-times","General relativity","Minkowski space-time"],"languages":["en"],"rights":["\"Creative
The University of Bradford theses are licenced under a Creative Commons Licence."],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/10454/3796","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Robinson, W.J."]},{"key":"dc:creator","label":"Author","values":["Griffin, G.K."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2009-10-28T16:29:40Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2009-10-28T16:29:40Z"]},{"key":"dc:date.issued","label":"Date","values":["2009-10-28T16:29:40Z"]},{"key":"dc:publisher.department","label":"Dc Publisher Department","values":["Postgraduate School of Studies in Mathematics."]},{"key":"dc:publisher.institution","label":"Dc Publisher Institution","values":["University of Bradford"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]},{"key":"dc:type.qualificationlevel","label":"Dc Type Qualificationlevel","values":["doctoral"]},{"key":"dc:type.qualificationname","label":"Dc Type Qualificationname","values":["PhD"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Asymptotic conformal Killing vectors","Asymptotically-flat space-times","General relativity","Minkowski space-time"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["\"Creative
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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]."]},{"key":"dc:title","label":"Title","values":["Conformal symmetries in special and general relativity.The derivation and interpretation of conformal symmetries and asymptotic conformal symmetries in Minkowski space-time and in some space-times of general relativity."]}]}],"canonical_facts":{"dc:contributor.advisor":["Robinson, W.J."],"dc:creator":["Griffin, G.K."],"dc:date.accessioned":["2009-10-28T16:29:40Z"],"dc:date.available":["2009-10-28T16:29:40Z"],"dc:date.issued":["2009-10-28T16:29:40Z"],"dc:description.abstract":["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]."],"dc:identifier.uri":["http://hdl.handle.net/10454/3796"],"dc:language.iso":["en"],"dc:publisher.department":["Postgraduate School of Studies in Mathematics."],"dc:publisher.institution":["University of Bradford"],"dc:rights":["\"Creative
The University of Bradford theses are licenced under a Creative Commons Licence."],"dc:subject":["Asymptotic conformal Killing vectors","Asymptotically-flat space-times","General relativity","Minkowski space-time"],"dc:title":["Conformal symmetries in special and general relativity.The derivation and interpretation of conformal symmetries and asymptotic conformal symmetries in Minkowski space-time and in some space-times of general relativity."],"dc:type":["Thesis"],"dc:type.qualificationlevel":["doctoral"],"dc:type.qualificationname":["PhD"]},"updated_at":"2026-07-24T01:14:44Z"}