dc.contributor |
Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV |
dc.contributor |
Román Roy, Narciso |
dc.contributor.author |
Ramos Olivé, Xavier |
dc.date |
2013-07 |
dc.identifier.uri |
http://hdl.handle.net/2099.1/19434 |
dc.language.iso |
eng |
dc.publisher |
Universitat Politècnica de Catalunya |
dc.rights |
Attribution-NonCommercial-ShareAlike 3.0 Spain |
dc.rights |
info:eu-repo/semantics/openAccess |
dc.rights |
http://creativecommons.org/licenses/by-nc-sa/3.0/es/ |
dc.subject |
Àrees temàtiques de la UPC::Matemàtiques i estadística |
dc.subject |
General relativity (Physics) |
dc.subject |
General relativity |
dc.subject |
Pseudoriemannian geometry |
dc.subject |
Einstein's equation |
dc.subject |
Special Relativity |
dc.subject |
Levi-Civitta connection |
dc.subject |
Semi-Riemannian geometry |
dc.subject |
Scwarzschild solution |
dc.subject |
Relativitat general (Física) |
dc.subject |
Classificació AMS::83 Relativity and gravitational theory::83C General relativity |
dc.title |
An Introduction to general relativity |
dc.title |
Una Introducción a la relatividad general |
dc.type |
info:eu-repo/semantics/bachelorThesis |
dc.description.abstract |
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. |
dc.description.abstract |
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. |