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General theory of relativity: mathematical elements and Hawking’s singularity theorem

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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2020, Director: Ricardo García López

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[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.

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cc-by-nc-nd (c) Sergi Novell Masot, 2020

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Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
General theory of relativity: mathematical elements and Hawking’s singularity theorem