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oai:recercat.cat:2099.1/194342025-07-22T22:46:03Zcom_2072_1033col_2072_452951

An Introduction to general relativity Una Introducción a la relatividad general Ramos Olivé, Xavier Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV Román Roy, Narciso Àrees temàtiques de la UPC::Matemàtiques i estadística General relativity (Physics) General relativity Pseudoriemannian geometry Einstein's equation Special Relativity Levi-Civitta connection Semi-Riemannian geometry Scwarzschild solution Relativitat general (Física) Classificació AMS::83 Relativity and gravitational theory::83C General relativity This bachelor's degree thesis is an introduction to the Theory of General Relativity (GR), a relativistic theory of gravity, from the point of view of a recently graduated mathematitian. The principles of GR are stated and some motivation on the formulation of the theory is provided. It is shown that freely-falling particles move along geodesics of spacetime and Einstein's equations are derived as a generalization of Newton's gravity. The uniqueness of Einstein's equations and the presence of the cosmological constant are discussed. The thesis concludes finding Schwarzschild solution by assuming that there exists a spherically symmetric metric that is a solution to Einstein's equations in vacuum and seeing what properties should this metric have. The boundary conditions imposed are the existence of a punctual uncharged mass at the origin and flatness of the metric at infinity. The result is a particular solution that can be applied in many contexts, such as in the Solar System. Se trata de hacer una presentación de los fundamentos, ecuaciones y algunos aspectos fenomenológicos de la Teoría General de la Relatividad, desde un punto de vista matemático formal. En particular:- Repasar algunos conceptos básicos de geometría diferencial.- Analizar los antecedentes y los postulados de la Relatividad General.- Obtener las ecuaciones de Einstein y estudiar su formulación variacional (lagrangiana de Hilbert).- Describir algunas consecuencias fenomenológicas y cosmológicas de la teoría. 2013-07 Bachelor thesis https://hdl.handle.net/2099.1/19434 eng http://creativecommons.org/licenses/by-nc-sa/3.0/es/ Open Access Attribution-NonCommercial-ShareAlike 3.0 Spain application/pdf Universitat Politècnica de Catalunya