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Principis variacionals en Relativitat General: lagrangianes de Hilbert i de Palatini

descriptionPublicationkeyboard_double_arrow_right Bachelor thesis 01 Jan 2021Publisher:Universitat Politècnica de Catalunya
Authors: Gabarró Solanas, Marta;

handle: 2117/336296

Principis variacionals en Relativitat General: lagrangianes de Hilbert i de Palatini

Abstract

La teoria de la Relativitat General és una teoria geomètrica de la gravetat que generalitza la teoria de la Relativitat Especial i les lleis newtonianes de la Gravitació, presentant la gravetat com la curvatura de l'espai-temps. Les equacions d'Einstein (EE) que determinen aquesta curvatura es poden obtenir a partir d'un principi variacional. En aquest treball, es resumeixen breument quines són les bases d'aquesta teoria i es deriven les EE a partir de la lagrangiana de Hilbert i les seves variants (amb presència de matèria-energia i amb Constant Cosmològica). També s'estudia una aproximació diferent a partir de la lagrangiana d'Einstein-Palatini i la relació amb el formalisme de Hilbert anterior.

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Keywords

Principi variacional, optimization::49S05 Variational principles of physics, Optimització matemàtica, Mathematical optimization, Classificació AMS::49 Calculus of variations and optimal control; optimization::49S05 Variational principles of physics, :49 Calculus of variations and optimal control [Classificació AMS], :49S05 Variational principles of physics [optimization], Relativitat General, Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica, Classificació AMS::49 Calculus of variations and optimal control, :Matemàtiques i estadística::Anàlisi matemàtica [Àrees temàtiques de la UPC], Lagrangiana d'Einstein-Palatini, Lagrangiana de Hilbert, Càlcul de variacions, Calculus of variations

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This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
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impulse
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