Geodesics and resonances of the Manko-Novikov spacetime
| dc.contributor.advisor | Brink, Jeandrew | en_ZA |
| dc.contributor.advisor | Scholtz, Frederik G. | en_ZA |
| dc.contributor.author | Geyer, Marisa | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Physics. | en_ZA |
| dc.date.accessioned | 2013-02-22T08:14:50Z | en_ZA |
| dc.date.accessioned | 2013-03-15T07:44:32Z | |
| dc.date.available | 2013-02-22T08:14:50Z | en_ZA |
| dc.date.available | 2013-03-15T07:44:32Z | |
| dc.date.issued | 2013-03 | en_ZA |
| dc.description | Thesis (MSc)--Stellenbosch University, 2013. | en_ZA |
| dc.description.abstract | ENGLISH ABSTRACT: In this thesis I study compact objects described by the Manko-Novikov spacetime. The Manko- Novikov spacetime is an exact solution to the Einstein Field Equations that allows objects to be black hole-like, but with a multipole structure di erent from Kerr black holes. The aim of the research is to investigate whether we will observationally be able to tell these bumpy black holes, if they exist, apart from traditional Kerr black holes. I explore the geodesic motion of a test probe in the Manko-Novikov spacetime. I quantify the motion using Poincar e maps and rotation curves. The Manko-Novikov spacetime admits regions with regular motion as well as regions with chaotic motion. The occurrence of chaos is correlated with orbits for which the characteristic frequencies are resonant. The new result presented in this thesis is a global characterisation of where resonances and thus chaos are likely to occur for all orbits. These calculations are performed in the Kerr spacetime, from which I obtain that low order resonances occur within 20 Schwarzschild radii (or 40M) of the compact object with mass M. By the KAM theorem, the occurrence of chaos is therefore limited to this region for all small perturbations from Kerr. These resonant events will be measurable in the Galactic Centre using eLISA. This con nement of low order resonances indicates that the frequency values of orbits of radii well outside of 20 Schwarzschild radii can be approximated using canonical perturbation theory. | en_ZA |
| dc.description.abstract | AFRIKAANSE OPSOMMING: In hierdie tesis word kompakte voorwerpe bestudeer soos omskryf deur die Manko-Novikov ruimtetyd. Die Manko-Novikov ruimtetyd is 'n eksakte oplossing van die Einstein Veldvergelykings. Die Manko-Novikov ruimtetyd formuleer gravitasiekolk-tipe voorwerpe waarvan die veelpool-struktuur afwyk van die tradisionele Kerr gravitasiekolk-struktuur. Die oogmerk van die navorsing is om vas te stel of ons met behulp van waarnemings hierdie bonkige gravitasiekolke van die tradisionele Kerr gravitasiekolke kan onderskei. Ek ondersoek die geodetiese beweging van 'n toetsmassa in die Manko-Novikov ruimtetyd. Die beweging word gekwanti seer met behulp van Poincar e afbeeldings en rotasiekrommes. In die Manko-Novikov ruimtetyd identi seer ek gebiede waarbinne re elmatige beweging voorkom asook gebiede waarbinne chaotiese bane voorkom. Die ontstaan van chaos word geassosieer met bane waarvan die fundamentele frekwensies resonant is. 'n Nuwe resultaat wat in hierdie tesis voorgehou word behels 'n globale karakterisering wat aandui waar resonansies en dus chaos na alle waarskynlikheid voorkom. Laasgenoemde berekeninge word vir die Kerr ruimtetyd uitgevoer. Hierdeur toon ek alle lae orde resonansies kom voor binne 20 Schwarzschild radii (of 40M) vanaf die kompakte voorwerp met mass M. Die KAM Stelling bepaal dan dat vir alle klein steurings toegepas op die Kerr ruimtetyd die voorkoms van chaos beperk sal wees tot bogenoemde gebied. Die resonansies binne hierdie gebied sal deur eLISA in die sentrum van die melkwegstelsel gemeet kan word. Hierdie beperking van lae orde resonansies tot 'n sekere afstand vanaf die kompakte voorwerp verseker dat die frekwensies van bane wat buite hierdie gebied val, akkuraat deur kanoniese steuringsteorie bepaal kan word. | af_ZA |
| dc.format.extent | xii, 84 p. : col. ill. | |
| dc.identifier.uri | http://hdl.handle.net/10019.1/80306 | |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | |
| dc.subject | Bumpy black holes | en_ZA |
| dc.subject | No hair theorems | en_ZA |
| dc.subject | Manko Novikov spacetime | en_ZA |
| dc.subject | Geodesic motion | en_ZA |
| dc.subject | Chaos | en_ZA |
| dc.subject | Resonance | en_ZA |
| dc.subject | Dissertations -- Physics | en_ZA |
| dc.subject | Theses -- Physics | en_ZA |
| dc.title | Geodesics and resonances of the Manko-Novikov spacetime | en_ZA |
| dc.type | Thesis | en_ZA |