Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
Cosmological Models and Singularities in General Relativity
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This is a thesis on general relativity. It analyzes dynamical properties of Einstein's field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas.

The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, which consists of five papers. The first two of those papers uses dynamical systems methods to analyze the simplest possible homogeneous model with two tilted perfect fluids with a linear equation of state. The third paper investigates the past asymptotic dynamics of barotropic multi-fluid models that approach a `silent and local' space-like singularity to the past. The fourth paper uses Hamiltonian methods to derive new monotone functions for the tilted Bianchi type II model that can be used to completely characterize the future asymptotic states globally. The last paper proves that there exists a full set of solutions to Einstein's field equations coupled to an ultra-stiff perfect fluid that has an initial singularity that is very much like the singularity in Friedman models in a precisely defined way.

Place, publisher, year, edition, pages
Karlstad: Karlstad University , 2011. , 90 p.
Series
Karlstad University Studies, ISSN 1403-8099 ; 2011:46
Keyword [en]
general relativity, Bianchi cosmology, singularities, dynamical systems, Fuchsian methods, Hamiltonian methods
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-8206ISBN: 978-91-7063-381-2 (print)OAI: oai:DiVA.org:kau-8206DiVA: diva2:440149
Public defence
2011-10-20, 11D 227, Karlstads universitet, Karlstad, 13:15 (English)
Opponent
Supervisors
Note

Status of the paper "Perfect Fluids and Generic Spacelike Singularities" has changed from manuscript to published since the thesis defense.

Available from: 2011-09-30 Created: 2011-09-09 Last updated: 2015-12-14Bibliographically approved
List of papers
1. Bianchi Type I Models with Two Tilted Fluids
Open this publication in new window or tab >>Bianchi Type I Models with Two Tilted Fluids
2008 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 25, no 22, 1-23 p.Article in journal (Refereed) Published
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-4909 (URN)10.1088/0264-9381/25/22/225013 (DOI)
Available from: 2009-11-16 Created: 2009-11-16 Last updated: 2017-12-12Bibliographically approved
2. Tilted Two-Fluid Bianchi Type I Models
Open this publication in new window or tab >>Tilted Two-Fluid Bianchi Type I Models
2009 (English)In: General Relativity and Gravitation, ISSN 0001-7701, E-ISSN 1572-9532, Vol. 41, 2707-2724 p.Article in journal (Refereed) Published
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-4910 (URN)10.1007/s10714-009-0799-5 (DOI)
Available from: 2009-11-16 Created: 2009-11-16 Last updated: 2017-12-12Bibliographically approved
3. Perfect Fluids and Generic Spacelike Singularities
Open this publication in new window or tab >>Perfect Fluids and Generic Spacelike Singularities
2010 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 27, no 2, 025013- p.Article in journal (Refereed) Published
Abstract [en]

We present the 1+3 Hubble-normalized conformal orthonormal frame approach to Einstein field equations, and specialize it to a source that consists of perfect fluids with general barotropic equations of state. We use this framework to give specific mathematical content to conjectures about generic spacelike singularities that were originally introduced by Belinskii, Khalatnikov and Lifshitz. Assuming that the conjectures hold, we derive results about how the properties of fluids and generic spacelike singularities affect each other.

National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-8209 (URN)10.1088/0264-9381/27/2/025013 (DOI)
Funder
Swedish Research Council, 621-2009-4163
Available from: 2011-09-09 Created: 2011-09-09 Last updated: 2017-12-08Bibliographically approved
4. Future Asymptotics of Tilted Bianchi Type II Cosmologies
Open this publication in new window or tab >>Future Asymptotics of Tilted Bianchi Type II Cosmologies
2010 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 27, 185006- p.Article in journal (Refereed) Published
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-8208 (URN)10.1088/0264-9381/27/18/185006 (DOI)
Available from: 2011-09-09 Created: 2011-09-09 Last updated: 2017-12-08Bibliographically approved
5. The Initial Singularity of Ultrastiff Perfect Fluid Spacetimes Without Symmetries
Open this publication in new window or tab >>The Initial Singularity of Ultrastiff Perfect Fluid Spacetimes Without Symmetries
2012 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, no 313, 385-403 p.Article in journal (Refereed) Published
Abstract [en]

We consider the Einstein equations coupled to an ultrastiff perfect fluid and prove the existence of a family of solutions with an initial singularity whose structure is that of explicit isotropic models. This family of solutions is ‘generic’ in the sense that it depends on as many free functions as a general solution, i.e., without imposing any symmetry assumptions, of the Einstein-Euler equations. The method we use is a that of a Fuchsian reduction.

National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-8216 (URN)10.1007/s00220-012-1496-x (DOI)000305678600005 ()
Available from: 2011-09-12 Created: 2011-09-12 Last updated: 2017-12-08Bibliographically approved

Open Access in DiVA

fulltext(751 kB)1353 downloads
File information
File name FULLTEXT03.pdfFile size 751 kBChecksum SHA-512
e5ca25e3040b0d84f7b8e36141f7a3547d5147825ade3765899b2a482eccf51dc7d290f5d0fdfdbfebf56c49f5f681f9c72423518ea928192fc4ee89636157ea
Type fulltextMimetype application/pdf

Search in DiVA

By author/editor
Sandin, Patrik
By organisation
Department of Physics and Electrical Engineering
Physical SciencesAstronomy, Astrophysics and Cosmology

Search outside of DiVA

GoogleGoogle Scholar
Total: 1353 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 400 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf