On higher dimensional Kerr-Schild spacetimes
| Název práce v češtině: | On higher dimensional Kerr-Schild spacetimes |
|---|---|
| Název v anglickém jazyce: | On higher dimensional Kerr-Schild spacetimes |
| Akademický rok vypsání: | 2007/2008 |
| Typ práce: | diplomová práce |
| Jazyk práce: | angličtina |
| Ústav: | Ústav teoretické fyziky (32-UTF) |
| Vedoucí / školitel: | Marcello Ortaggio |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 10.07.2009 |
| Datum zadání: | 10.07.2009 |
| Datum a čas obhajoby: | 24.09.2009 00:00 |
| Datum odevzdání elektronické podoby: | 05.08.2009 |
| Datum odevzdání tištěné podoby: | 05.08.2009 |
| Datum proběhlé obhajoby: | 24.09.2009 |
| Oponenti: | prof. RNDr. Jiří Podolský, CSc., DSc. |
| Zásady pro vypracování |
| Thanks to recent advances in string theory and the advent of large extra dimension scenarios, gravity in higher dimensions has developed rapidly into an active and interdisciplinary area of ongoing studies. It has applications in fundamental theories as well as in phenomenology.
The present project concerns classical aspects of gravity in more than four dimensions, in particular exact solutions and analytic methods. The applicant will first become familiar with advanced methods of standard general relativity, such as the Petrov classification and its applications (see e.g. Petrov and Stephani et al. books). Subsequently, he will study very recent developments of similar techniques in higher dimensions (such as those in the Coley et al. paper). Finally, the core of the work will be an original investigations of open problems of higher dimensional gravity, based on such methods. In particular, the focus will be on the algebraic type of the Weyl tensor, "optical" and geometrical properties, and classification of solutions of the Einstein equations. |
| Seznam odborné literatury |
| A. Coley, Classification of the Weyl Tensor in Higher Dimensions and Applications, arXiv:0710.1598v1 [gr-qc]
A. Coley, R. Milson, V. Pravda, A. Pravdova, Classification of the Weyl Tensor in Higher Dimensions, Class. Q. Grav. 21:L35, 2004 H. Stephani et al., Exact Solutions of Einstein's Field Equations (CUP, Cambrige 2003) A. Z. Petrov, Einstein spaces, (OUP, Oxford 1969) R. Myers, M. Perry, Black Holes in Higher Dimensional Space-Times, Annals Phys. 172:304, 1986 |
| Předběžná náplň práce |
| During the past decade, there has been a significant increase in interest in the properties of gravity in more than four spacetime dimensions. This largely stems from the recognition of the relevance of black holes to fundamental theories such as string theory, along with the idea of large or infinite extra dimensions recently resurrected by braneworld models of TeV gravity. Several higher-dimensional solutions of classical General Relativity have been known for some time. However, recent investigations have shown that, even at the classical level, gravity in higher dimensions exhibits much richer dynamics than in four dimensions. In fact, in spite of remarkable advances in the past few years, various features of gravity in higher dimensions have still to be explored. The present thesis will study geometric and analytic properties of solutions of Einstein's field equations in higher dimensions. |
| Předběžná náplň práce v anglickém jazyce |
| During the past decade, there has been a significant increase in interest in the properties of gravity in more than four spacetime dimensions. This largely stems from the recognition of the relevance of black holes to fundamental theories such as string theory, along with the idea of large or infinite extra dimensions recently resurrected by braneworld models of TeV gravity. Several higher-dimensional solutions of classical General Relativity have been known for some time. However, recent investigations have shown that, even at the classical level, gravity in higher dimensions exhibits much richer dynamics than in four dimensions. In fact, in spite of remarkable advances in the past few years, various features of gravity in higher dimensions have still to be explored. The present thesis will study geometric and analytic properties of solutions of Einstein's field equations in higher dimensions. |