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The Einstein Field Equations: on semi-Riemannian manifolds, and the Schwarzschild solutionPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2012 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
##### Abstract [en]

##### Place, publisher, year, edition, pages

2012.
##### Keyword [en]

Differential geometry, semi-Riemannian manifolds, Einstein field equations
##### National Category

Mathematics Other Mathematics
##### Identifiers

URN: urn:nbn:se:umu:diva-61321OAI: oai:DiVA.org:umu-61321DiVA: diva2:566736
##### Educational program

Bachelor of Science in Physics and Applied Mathematics
##### Uppsok

Physics, Chemistry, Mathematics

#####

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Available from: 2013-02-27 Created: 2012-11-09 Last updated: 2015-06-09Bibliographically approved

Semi-Riemannian manifolds is a subject popular in physics, with applications particularly to modern gravitational theory and electrodynamics. Semi-Riemannian geometry is a branch of differential geometry, similar to Riemannian geometry. In fact, Riemannian geometry is a special case of semi-Riemannian geometry where the scalar product of nonzero vectors is only allowed to be positive. This essay approaches the subject from a mathematical perspective, proving some of the main theorems of semi-Riemannian geometry such as the existence and uniqueness of the covariant derivative of Levi-Civita connection, and some properties of the curvature tensor. Finally, this essay aims to deal with the physical applications of semi-Riemannian geometry. In it, two key theorems are proven - the equivalenceof the Einstein field equations, the foundation of modern gravitational physics, and the Schwarzschild solution to the Einstein field equations. Examples of applications of these theorems are presented.

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