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http://hdl.handle.net/2445/177883
Title: | General theory of relativity: mathematical elements and Hawking’s singularity theorem |
Author: | Novell Masot, Sergi |
Director/Tutor: | García López, Ricardo, 1962- |
Keywords: | Varietats diferenciables Treballs de fi de grau Geometria diferencial Relativitat general (Física) Differentiable manifolds Bachelor's theses Differential geometry General relativity (Physics) |
Issue Date: | 16-Jun-2020 |
Abstract: | [en] In this work, we study Riemannian and pseudo-Riemannian manifolds and their main properties. From them, we examine the special and general theories of relativity, and see how they arise from modelling space-time as special kinds of pseudoRiemannian manifolds, the Lorentzian manifolds. Within this theory, we are able to give a rigorous formulation of the fundamental properties of cosmology and the Schwarzschild space-time. We also wish to relate the behaviour of geodesics in a manifold with the intrinsic structure of the manifold. This results in the formulation of the Hopf-Rinow theorem in the case of Riemannian manifolds, and the Hawking singularity theorem, in Lorentzian manifolds. |
Note: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ricardo García López |
URI: | http://hdl.handle.net/2445/177883 |
Appears in Collections: | Treballs Finals de Grau (TFG) - Matemàtiques |
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File | Description | Size | Format | |
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177883.pdf | Memòria | 840.32 kB | Adobe PDF | View/Open |
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