Rotko, Iisakki (2023) Classifications of Galilean and Carrollian Spacetimes with and without indices. Master's Thesis / Essay, Physics.
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Abstract
Non-Lorentzian geometries have resurfaced recently as a topic of interest in various fields, including non-relativistic string theory, cosmology, and condensed matter physics. Two specific non-Lorentzian geometries have been of particular interest: Galilean and Carrollian ones. Recently, the spacetimes whose structure is dictated by these groups were classified for particles and Strings. Following two approaches, inspired by the mathematics and physics literatures on the topic, we will extend this classification to cover generic p-brane foliations, and provide the geometric interpretation corresponding to the classification. Both methods will employ an approach of finding the possible forms of \textit{intrinsic torsion} that the spacetimes may possess, as well as a mathematical tool called the Spencer differential. We find five potential classes of intrinsic torsion and five corresponding constraints on the geometry. Finally, we will derive the corresponding theories of gravity, and demonstrate that it matters whether a limit to a theory is taken from a second or first-order formulation of general relativity.
| Item Type: | Thesis (Master's Thesis / Essay) |
|---|---|
| Supervisor name: | Bergshoeff, E.A. and Meerburg, P.D. |
| Degree programme: | Physics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 12 Jul 2023 11:23 |
| Last Modified: | 12 Jul 2023 11:23 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/30576 |
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