Gravitační vlny v kosmologii

• Thesis title in Czech: Gravitační vlny v kosmologii
• Thesis title in English: Gravitational waves in cosmology
• Key words: Gravitační vlny, kosmologické modely, perturbace, vysokofrekvenční aproximace.
• English key words: Gravitational waves, cosmological models, perturbation, high-frequency approximation.
• Academic year of topic announcement: 2013/2014
• Thesis type: diploma thesis
• Thesis language: čeština
• Department: Institute of Theoretical Physics (32-UTF)
• Supervisor: doc. RNDr. Otakar Svítek, Ph.D.
• Author: hidden - assigned and confirmed by the Study Dept.
• Date of registration: 10.04.2014
• Date of assignment: 10.04.2014
• Confirmed by Study dept. on: 23.04.2014
• Date and time of defence: 12.02.2016 00:00
• Date of electronic submission: 04.12.2015
• Date of submission of printed version: 04.12.2015
• Date of proceeded defence: 12.02.2016
• Opponents: doc. RNDr. Martin Žofka, Ph.D.

Guidelines

Student se seznámí se složitějšími kosmologickými modely nad rámec FLRW včetně prostoročasů s netriviální topologií, např. T^3. Zároveň prostuduje různé druhy popisu gravitačních vln - jak exaktní, tak aproximativní. Soustředí se na Isaacsonovu vysokofrekvenční aproximaci zejména s ohledem na ovlivnění pozadí přítomností vln. Následně prostuduje tento problém za použití konkrétních kosmologických pozadí. Pro zjednodušení je možné uvažovat šíření pouze ve vhodně zvoleném směru a použít WKB aproximaci. V takovém případě je pro konzistentní řešení problému nutné, aby pozadí připouštělo nulovou tekutinu. Dále je možné studovat vliv vln na vlastnosti pozadí, např. typ singularity s ohledem na BKL domněnku.

References

R.A. Isaacson: Gravitational Radiation in the Limit of High Frequency I., II., Phys. Rev. 166 (1968) 1263–1280
J. Podolský, O. Svítek: Some high-frequency gravitational waves related to exact radiative spacetimes, Gen. Rel. Grav. 36 (2004) 387. URL: http://arxiv.org/abs/gr-qc/0310084v1
R. Wald: General Relativity, University of Chicago Press (1984)
A. Krasinski: Inhomogeneous cosmological models, Cambridge university press (1997)
H. Ringström: Cosmic Censorship for Gowdy Spacetimes, Living Rev. Relativity 13 (2010) 2. URL: http://www.livingreviews.org/lrr-2010-2
Ch. Charach, S. Malin: Cosmological model with gravitational and scalar waves, Phys. Rev. D 19 (1979) 1058–1064

Preliminary scope of work in English

Although directly undetected so far, gravitational waves play an important role in the development of general relativity. Not only they might provide a new astronomical window to the universe but they play a role in models curved dominantly by their presence. These spacetimes are found among both exact solutions and using approximative techniques - namely high-frequency perturbations. Since exact radiative spacetimes posses preferred null direction they may serve as useful background for adding high-frequency radiation and thus study, for example, a stability of different properties of these spacetimes. One may also study radiation in asymptotically non-flat blackhole models with cosmological exterior. Substantial interest regarding topologically nontrivial models is devoted to the Gowdy universe, namely its T^3 version. The analysis in the simple polarized case was already carried out, but more interesting situations cannot be treated exactly. In such a situation perturbative approach might help in gaining insight into an exact solution behaviour.