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The Einstein Field Equations: on semi-Riemannian manifolds, and the Schwarzschild solution
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
2012 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

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.

Place, publisher, year, edition, pages
Keyword [en]
Differential geometry, semi-Riemannian manifolds, Einstein field equations
National Category
Mathematics Other Mathematics
URN: urn:nbn:se:umu:diva-61321OAI: diva2:566736
Educational program
Bachelor of Science in Physics and Applied Mathematics
Physics, Chemistry, Mathematics
Available from: 2013-02-27 Created: 2012-11-09 Last updated: 2015-06-09Bibliographically approved

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