General theory of relativity: mathematical elements and Hawking’s singularity theorem
| Autor: | Novell Masot, Sergi |
|---|---|
| Přispěvatelé: | García López, Ricardo, 1962 |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
General Relativity and Quantum Cosmology
Bachelor's thesis Geometria diferencial Relativitat general (Física) Varietats diferenciables Bachelor's theses General relativity (Physics) Differential geometry Mathematics::Differential Geometry Treballs de fi de grau Mathematics::Geometric Topology Mathematics::Symplectic Geometry Differentiable manifolds |
| Zdroj: | Dipòsit Digital de la UB Universidad de Barcelona |
| Popis: | Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ricardo García López [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. |
| Databáze: | OpenAIRE |
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