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The Initial Singularity of Ultrastiff Perfect Fluid Spacetimes Without Symmetries
University of Vienna, Faculty of Physics, Gravitational Physics, Austria.
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering. (Fysik)
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.

Place, publisher, year, edition, pages
2012. no 313, 385-403 p.
National Category
Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
URN: urn:nbn:se:kau:diva-8216DOI: 10.1007/s00220-012-1496-xISI: 000305678600005OAI: oai:DiVA.org:kau-8216DiVA: diva2:440126
Available from: 2011-09-12 Created: 2011-09-12 Last updated: 2015-12-29Bibliographically approved
In thesis
1. Cosmological Models and Singularities in General Relativity
Open this publication in new window or tab >>Cosmological Models and Singularities in General Relativity
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
general relativity, Bianchi cosmology, singularities, dynamical systems, Fuchsian methods, Hamiltonian methods
National Category
Physical Sciences Astronomy, Astrophysics and Cosmology
Research subject
Physics
Identifiers
urn:nbn:se:kau:diva-8206 (URN)978-91-7063-381-2 (ISBN)
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

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Citation style
  • apa
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