Constructing initial data on past null infinity.
| dc.contributor.author | Barrer, Merlyn | |
| dc.date.accessioned | 2025-01-07T21:07:11Z | |
| dc.date.available | 2025-01-07T21:07:11Z | |
| dc.date.issued | 2024 | |
| dc.description.abstract | We consider the scattering of gravitational waves in asymptotically flat space-times. Such a space-time can be conformally compactified to introduce a conformal boundary, where the ingoing wave is defined on a part of the conformal boundary called past null infinity. In this setting, Einstein’s equations take the form of the conformal field equations, with the ingoing wave on past null infinity representing the physical degree of freedom for the system. The aim of this thesis is to develop methods for constructing initial data sets for the conformal field equations on past null infinity in the linearised setting. We describe the mathematical framework for the conformal field equations, and linearise around a Minkowski background. We obtain equations on past null infinity for the initial data, in both the F-gauge and a different gauge in which we can access all of past null infinity. From this we obtain new conditions on the ingoing wave for the initial data to be regular. Finally, we develop numerical methods to solve the equations for the initial data, and apply these successfully to construct regular initial data sets on past null infinity. | |
| dc.identifier.uri | https://hdl.handle.net/10092/107861 | |
| dc.identifier.uri | https://doi.org/10.26021/15573 | |
| dc.language | English | |
| dc.language.iso | en | |
| dc.rights | All Right Reserved | |
| dc.rights.uri | https://canterbury.libguides.com/rights/theses | |
| dc.title | Constructing initial data on past null infinity. | |
| dc.type | Theses / Dissertations | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | University of Canterbury | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Mathematical Sciences | |
| uc.bibnumber | in1403186 | |
| uc.college | Faculty of Engineering |