<div class="csl-bib-body">
<div class="csl-entry">Fuchs, A. (2014). <i>Null canonical formulation and integrability of cylindrical gravitational waves</i> [Diploma Thesis, Technische Universität Wien]. reposiTUm. https://doi.org/10.34726/hss.2014.23869</div>
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dc.identifier.uri
https://doi.org/10.34726/hss.2014.23869
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/5657
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dc.description
Abweichender Titel laut Übersetzung der Verfasserin/des Verfassers
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dc.description.abstract
The gravitational field in four dimensional spacetime may be described using free initial data on a pair of intersecting null hypersurfaces swept out by the future null normal geodesics to their two dimensional intersection surface. A Poisson bracket on such initial data was calculated by Michael Reisenberger. The expressions obtained are tractable but still rather intricate, and it is not at all obvious how this bracket might be quantized. A change of variables that simplifies the bracket would thus be desirable. The bracket does have the feature (reflecting causality) that it is non-zero only between data lying on the same generating null geodesic, and that it only depends on the data on this generator. That is, the data on each generator forms an essentially autonomous Poisson algebra. The limited role of the two transverse dimensions suggests that the Poisson algebra would remain substantially the same in a symmetry reduced model in which the transverse dimensions have been eliminated. Here this expectation is confirmed in the context of cylindrically symmetric gravitational waves. Specifically, the Poisson algebra of the metric variables in free null initial data for cylindrically symmetric gravitational waves is obtained, and it is found to be essentially identical to the bracket on the metric sector of the initial data found in by Reisenberger. Then, using the integrability of the dynamics of cylindrically symmetric gravitational waves an explicit transformation from metric data on a null hypersurface to so called "monodromy data", a one parameter family of unimodular matrices, is obtained. The Poisson brackets of the monodromy data are then obtained from that of the null data. These have been obtained earlier via another route in a slightly more restricted context. They are quite simple, and what is more, a unique preferred quantization is known. It is also demonstrated that the transformation to monodromy data is invertible. Aside from these original results extensive background material is presented, including a review of the Geroch group of symmetries in cylindrically symmetrical gravity. The original results presented here are joint work with Michael Reisenberger.
en
dc.language
English
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dc.language.iso
en
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dc.rights.uri
http://rightsstatements.org/vocab/InC/1.0/
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dc.subject
Allgemeine Relativitätstheorie
de
dc.subject
lichtartige Anfangsdaten
de
dc.subject
Poisson Klammer
de
dc.subject
Integrables System
de
dc.subject
Monodromie Matrix
de
dc.subject
General relativity
en
dc.subject
Null initial data
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dc.subject
Poisson bracket
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dc.subject
Integrabel System
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dc.subject
Monodromie Matrix
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dc.title
Null canonical formulation and integrability of cylindrical gravitational waves
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dc.type
Thesis
en
dc.type
Hochschulschrift
de
dc.rights.license
In Copyright
en
dc.rights.license
Urheberrechtsschutz
de
dc.identifier.doi
10.34726/hss.2014.23869
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dc.contributor.affiliation
TU Wien, Österreich
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dc.rights.holder
Andreas Fuchs
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tuw.version
vor
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tuw.thesisinformation
Technische Universität Wien
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tuw.publication.orgunit
E136 - Institut für Theoretische Physik
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dc.type.qualificationlevel
Diploma
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dc.identifier.libraryid
AC11460883
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dc.description.numberOfPages
159
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dc.identifier.urn
urn:nbn:at:at-ubtuw:1-75186
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dc.thesistype
Diplomarbeit
de
dc.thesistype
Diploma Thesis
en
dc.rights.identifier
In Copyright
en
dc.rights.identifier
Urheberrechtsschutz
de
tuw.advisor.staffStatus
staff
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item.fulltext
with Fulltext
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item.mimetype
application/pdf
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item.openairecristype
http://purl.org/coar/resource_type/c_bdcc
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item.cerifentitytype
Publications
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item.openairetype
master thesis
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item.grantfulltext
open
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item.openaccessfulltext
Open Access
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item.languageiso639-1
en
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crisitem.author.dept
E104-03 - Forschungsbereich Differentialgeometrie und geometrische Strukturen
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crisitem.author.parentorg
E104 - Institut für Diskrete Mathematik und Geometrie