Symmetry reduction of gravitational Lagrangians
| Název práce v češtině: | Symetrická redukce gravitačních Lagrangiánů |
|---|---|
| Název v anglickém jazyce: | Symmetry reduction of gravitational Lagrangians |
| Klíčová slova: | obecná teorie relativity|modifikovaná gravitace|symetrická redukce|Lagrangián|Weylův trik |
| Klíčová slova anglicky: | general relativity|modified gravity|symmetry reduction|Lagrangian|Weyl trick |
| Akademický rok vypsání: | 2023/2024 |
| Typ práce: | bakalářská práce |
| Jazyk práce: | angličtina |
| Ústav: | Ústav teoretické fyziky (32-UTF) |
| Vedoucí / školitel: | Mgr. Ivan Kolář, Ph.D. |
| Řešitel: | skrytý - zadáno a potvrzeno stud. odd. |
| Datum přihlášení: | 03.11.2023 |
| Datum zadání: | 16.11.2023 |
| Datum potvrzení stud. oddělením: | 20.11.2023 |
| Zásady pro vypracování |
| The student should become familiar with the symmetry reduction of Lagrangian densities for general relativity and its higher-derivative modifications, i.e., the Weyl trick and its generalizations beyond the spherically symmetric static case [1,2,3]. The main objective is to (re)derive the reduced Lagrangians and the field equations in the cases that have not been analyzed in the literature before or presented in full detail. They should be contrasted to the reduced field equations (which also have to be calculated) and solved if possible.
Optionally, the student may also delve deeper into the mathematics behind the symmetry reduction of Lagrangians known as the principle of symmetric criticality [4], review it, and/or analyze the conditions under which the symmetry reduction commutes with the variation for chosen group actions from [5]. |
| Seznam odborné literatury |
| [1] H. Weyl, The theory of gravitation, Annalen Phys. 54, 117 (1917)
[2] S. Deser and B. Tekin, Shortcuts to high symmetry solutions in gravitational theories, Class. Quant. Grav. 20, 4877 (2003), arXiv:gr-qc/0306114. [3] S. Deser and J. Franklin, Schwarzschild and Birkhoff a la Weyl, Am. J. Phys. 73, 261 (2005), arXiv:gr-qc/0408067. [4] 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. [5] A. Z. Petrov, Einstein Spaces (1969). |