Přesná řešení kvadratické gravitace prostřednictvím symetriemi redukovaných Lagrangiánů
| Název práce v češtině: | Přesná řešení kvadratické gravitace prostřednictvím symetriemi redukovaných Lagrangiánů |
|---|---|
| Název v anglickém jazyce: | Exact solutions of quadratic gravity via symmetry-reduced Lagrangians |
| Akademický rok vypsání: | 2024/2025 |
| Typ práce: | diplomová práce |
| Jazyk práce: | |
| Ústav: | Ústav teoretické fyziky (32-UTF) |
| Vedoucí / školitel: | Mgr. Ivan Kolář, Ph.D. |
| Řešitel: |
| Zásady pro vypracování |
| The student should become familiar with the symmetry reduction of gravitational Lagrangians [1] and its justification by the principle of symmetric criticality (PSC) [2]. Together, this provides rigorous reformulation of the Weyl trick [3] and presents an interesting shortcut in the derivation of exact solutions of general relativity and its modifications [4]. If satisfied, the principle of symmetric criticality guarantees that the field equations of the symmetry-reduced Lagrangians are equivalent to the symmetry-reduced field equations. As a part of the review, the student should verify the validity and violation of PSC for some infinitesimal group actions (by checking the conditions and by explicit comparison of the obtained field equations).
The main objective is to re-derive known exact solutions of general relativity and quadratic gravity and attempt to find new ones using the methods described in [1-4]. The solutions can be looked for within the PSC-compatible infinitesimal group actions from [1] either by hand and/or with the help of the code developed for [1] (employing the xAct package for Wolfram Mathematica). Depending on the results, it should be compared with the literature and interpreted appropriately, e.g., [5,6]. |
| Seznam odborné literatury |
| [1] G. Frausto, I. Kolar, T. Malek, C. Torre, Symmetry reduction of gravitational Lagrangians, in preparation.
[2] M. E. Fels and C. G. Torre, The Principle of symmetric criticality in general relativity, Class. Quant. Grav. 19, 641 (2002), arXiv:gr-qc/0108033. [3] H. Weyl, The theory of gravitation, Annalen Phys. 54, 117 (1917). [4] S. Deser and B. Tekin, Shortcuts to high symmetry solutions in gravitational theories, Class. Quant. Grav. 20, 4877 (2003), arXiv:gr-qc/0306114. [5] H. Stephani, D. Kramer, M. MacCallum, C. Hoenselaers, and E. Herlt, Cambridge monographs on mathematical physics: Exact solutions of Einstein’s field equations, 2nd ed. (Cambridge University Press, Cambridge, England, 2009). [6] V. Pravda, A. Pravdová, J. Podolsky, R. Svarc, Exact solutions to quadratic gravity, Phys. Rev. D 95, 084025 (2017), arXiv:1606.02646 [gr-qc]. |