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Future stability of the Einstein-Maxwell-Scalar field system and non-linear wave equations coupled to generalized massive-massless Vlasov equationsPrimeFaces.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)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Stockholm: KTH Royal Institute of Technology, 2012. , vi, 19 p.
##### Series

Trita-MAT. MA, ISSN 1401-2278 ; 12:03
##### National Category

Mathematical Analysis Geometry
##### Identifiers

URN: urn:nbn:se:kth:diva-93891ISBN: 978-91-7501-294-0OAI: oai:DiVA.org:kth-93891DiVA: diva2:524534
##### Public defence

2012-05-21, Sal F3, Lindstedtsvägen 26, KTH, 10:00 (English)
##### Opponent

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##### Supervisors

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#####

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##### Note

QC 20120503Available from: 2012-05-03 Created: 2012-05-02 Last updated: 2012-05-03Bibliographically approved
##### List of papers

This thesis consists of two articles related to mathematical relativity theory.

In the first article we prove future stability of certain spatially homogeneous solutionsto Einstein’s field equations. The matter model is assumed to consist of an electromagnetic field and a scalar field with a potential creating an accelerated expansion. Beside this, more general properties concerning Einstein’s field equation coupled to a scalar field and an electromagnetic field are settled. The most important of these questions are the existence of a maximal globally hyperbolic development and the Cauchy stability of solutions to the initial value problem.

In the second article we consider Einstein’s field equations where the matter model consists of two momentum distribution functions. The first momentum distribution function represents massive matter, for instance galactic dust, and the second represents massless matter, for instance radiation. Furthermore, we require that each of the momentum distribution functions shall satisfy the Vlasov equation. This means that the momentum distribution functions represent collisionless matter. If Einstein’s field equations with such a matter model is expressed in coordinates and if certain gauges are fixed we get a system of integro-partial differential equations we shall call non-linear wave equations coupled to generalized massive-massless Vlasov equations. In the second article we prove that the initial value problem associated to this kind of equations has a unique local solution.

1. Future Stability of the Einstein-Maxwell-Scalar Field System$(function(){PrimeFaces.cw("OverlayPanel","overlay420915",{id:"formSmash:j_idt503:0:j_idt507",widgetVar:"overlay420915",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. Non-linear wave equations coupled to generalized massive-massless Vlasov equations$(function(){PrimeFaces.cw("OverlayPanel","overlay523839",{id:"formSmash:j_idt503:1:j_idt507",widgetVar:"overlay523839",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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