Axial symmetry and transverse trace-free tensors in numerical relativity

Simple item page
dc.contributor.advisorÓ Murchadha, Niall
dc.contributor.authorConboye, Rory P. A.
dc.contributor.funderScience Foundation Irelanden
dc.date.accessioned2012-02-21T11:38:56Z
dc.date.available2012-02-21T11:38:56Z
dc.date.issued2012-02
dc.date.submitted2012-02-14
dc.description.abstractTransverse trace-free (TT) tensors play an important role in the initial conditions of numerical relativity, containing two of the component freedoms. Expressing a TT tensor entirely, by the choice of two scalar potentials, is not a trivial task however. Assuming the added condition of axial symmetry, expressions are given in both spherical and cylindrical coordinates, for TT tensors in flat space. A coordinate relation is then calculated between the scalar potentials of each coordinate system. This is extended to a non-flat space, though only one potential is found. The remaining equations are reduced to form a second order partial differential equation in two of the tensor components. With the axially symmetric flat space tensors, the choice of potentials giving Bowen-York conformal curvatures, are derived. A restriction is found for the potentials which ensure an axially symmetric TT tensor, which is regular at the origin, and conditions on the potentials, which give an axially symmetric TT tensor with a spherically symmetric scalar product, are also derived. A comparison is made of the extrinsic curvatures of the exact Kerr solution and numerical Bowen-York solution for axially symmetric black hole space-times. The Brill wave, believed to act as the difference between the Kerr and Bowen-York space-times, is also studied, with an approximate numerical solution found for a mass-factor, under different amplitudes of the metric.en
dc.description.statusNot peer revieweden
dc.description.versionAccepted Versionen
dc.format.mimetypeapplication/pdfen
dc.identifier.citationConboye, Rory P.A. 2012. Axial Symmetry and Transverse Trace-Free Tensors in Numerical Relativity. PhD Thesis, University College Cork.en
dc.identifier.urihttps://hdl.handle.net/10468/527
dc.language.isoenen
dc.publisherUniversity College Corken
dc.rights© 2012, Rory Patrick Albert Conboyeen
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/en
dc.subjectNumerical relativityen
dc.subjectInitial value problemen
dc.subject.lcshRelativity (Physics)en
dc.subject.lcshGeometry, Differentialen
dc.subject.lcshMathematical physicsen
dc.titleAxial symmetry and transverse trace-free tensors in numerical relativityen
dc.typeDoctoral thesisen
dc.type.qualificationlevelDoctoralen
dc.type.qualificationnamePhD (Physics)en
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
ConboyeRPA_PhD2012.pdf
Size:
1.6 MB
Format:
Adobe Portable Document Format
Description:
Full text available
Download
License bundle
Now showing 1 - 2 of 2
Thumbnail Image
Name:
license.txt
Size:
5.75 KB
Format:
Item-specific license agreed upon to submission
Description:
Download
Thumbnail Image
Name:
RC_PhDLicence.pdf
Size:
243.68 KB
Format:
Adobe Portable Document Format
Description:
License
Collections
Doctoral Theses
College of Science, Engineering and Food Science - Doctoral Theses
Physics - Doctoral Theses