# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2021, Director: Àlex Haro

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[en] We begin with a brief tensor development in semi-Riemannian geometry. We will expose mathematical objects such as the Ricci tensor, the curvature tensor or the Levi-Civita connection, that will serve us for the nature presentation of Einstein’s tensor. Immediately, due to the theoretical foundation of Cosmological Principle, as well as the hypothesis of the perfect fluid, we will deduce Einstein’s field equations.
We will solve the Einstein equations, focusing on three complementary models that describe the shape and dynamics of the space-time structure: Schwarzschild’s solution, Kerr’s solution and Friedmann’s solutions. We will highlight Friedmann’s solutions analyzing different models of the Universe according to the cosmological densities in order to expose the destination and the end of the different universes: an analysis on dynamics.
Finally, the nature of the Theory of Causality is exposed in an abbreviated and summarized way. The study of Lorentz geometry will allow us to know in first-hand the theorems of existence of space-time singularities: one of the main contributions of the famous mathematician-physicist Penrose, and the reason why in this year 2019 he has been awarded the Nobel Prize in Physics.

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cc-by-nc-nd (c) Alejandro León Pérez, 2021

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Treballs Finals de Grau (TFG) - Matemàtiques