Symmetry reduction of gravitational Lagrangians
| Thesis title in Czech: | Symetrická redukce gravitačních Lagrangiánů |
|---|---|
| Thesis title in English: | Symmetry reduction of gravitational Lagrangians |
| Key words: | obecná teorie relativity|modifikovaná gravitace|symetrická redukce|Lagrangián|Weylův trik |
| English key words: | general relativity|modified gravity|symmetry reduction|Lagrangian|Weyl trick |
| Academic year of topic announcement: | 2023/2024 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | angličtina |
| Department: | Institute of Theoretical Physics (32-UTF) |
| Supervisor: | Mgr. Ivan Kolář, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 03.11.2023 |
| Date of assignment: | 16.11.2023 |
| Confirmed by Study dept. on: | 20.11.2023 |
| Guidelines |
| 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]. |
| References |
| [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). |