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Stellar Models in General Relativity
Stockholm University, Faculty of Science, Department of Physics.
2003 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Neutron stars are some of the most fascinating objects in Nature. Essentially all aspects of physics seems to be represented inside them. Their cores are likely to contain deconfined quarks, hyperons and other exotic phases of matter in which the strong interaction is the dominant force. The inner region of their solid crust is penetrated by superfluid neutrons and their magnetic fields may reach well over 1012 Gauss. Moreover, their extreme mean densities, well above the densities of nuclei, and their rapid rotation rates makes them truly relativistic both in the special as well as in the general sense. This thesis deals with a small subset of these phenomena. In particular the exciting possibility of trapping of gravita-tional waves is examined from a theoretical point of view. It is shown that the standard condition R < 3M is not essential to the trapping mechanism. This point is illustrated using the elegant tool provided by the optical geometry. It is also shown that a realistic equation of state proposed in the literature allows stable neutron star models with closed circular null orbits, something which is closely related to trapped gravitational waves. Furthermore, the general relativistic theory of elasticity is reviewed and applied to stellar models. Both static equilibrium as well as radially oscillating configurations with elasticsources are examined. Finally, Killing tensors are considered and their applicability to modeling of stars is discussed

Place, publisher, year, edition, pages
Stockholm: Fysikum , 2003. , 73 p.
Keyword [en]
General relativity, compact objects
Keyword [sv]
neutron stars
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-13ISBN: 91-7265-746-4 (print)OAI: oai:DiVA.org:su-13DiVA: diva2:189817
Public defence
2003-10-17, FD5, AlbaNova niversitetscentrum, Roslagstullsbacken 21, Stockholm, 10:00
Opponent
Supervisors
Available from: 2003-09-25 Created: 2003-09-25Bibliographically approved
List of papers
1. Compact stellar objects with multiple neck optical geometries
Open this publication in new window or tab >>Compact stellar objects with multiple neck optical geometries
2000 (English)Article in journal (Refereed) Submitted
Abstract [en]

Ultra compact stellar models with a two-zone uniform density equation of state are considered. They are shown to provide neat examples of optical geometries exhibiting double necks, implying that the gravitational wave potential has a double well structure.

Keyword
general relativity, relativistic stars, gravitational waves
National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-22958 (URN)
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2011-06-17Bibliographically approved
2. Ultracompact stars with multiple necks
Open this publication in new window or tab >>Ultracompact stars with multiple necks
2002 (English)In: Modern Physics Letters A, ISSN 0217-7323, E-ISSN 1793-6632, Vol. 17, no 4, 197-203 p.Article in journal (Refereed) Published
Abstract [en]

We discuss ultracompact stellar objects which have multiple necks in their optical geometry. There are in fact physically reasonable equations of state for which the number of necks can be arbitrarily large. The proofs of these statements rely on a recent regularized formulation of the field equations for static spherically symmetric models due to Nilsson and Uggla. We discuss in particular the equation of state p = rho; - ρs which plays a central role in this context.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-22959 (URN)
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2017-12-13Bibliographically approved
3. Constructing stellar objects with multiple necks
Open this publication in new window or tab >>Constructing stellar objects with multiple necks
2001 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 18, no 5, 817-832 p.Article in journal (Refereed) Published
Abstract [en]

We discuss the construction of perfect fluid stellar objects having optical geometries with multiple necks corresponding to spatially closed unstable lightlike geodesics. We prove that physically reasonable equations of state can give rise to stellar equilibria with arbitrarily many necks. We also show how a first-order phase transition can give rise to quite pronounced secondary necks. The analysis is carried out using a modification of a recent dynamical systems formulation of the TOV equations due to Nilsson and Uggla. Our reformulation allows for a very general family of equations of state including, for example, phase transitions.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-22960 (URN)10.1088/0264-9381/18/5/305 (DOI)
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2017-12-13Bibliographically approved
4. A unified treatment of quartic invariants at fixed and arbitrary energy
Open this publication in new window or tab >>A unified treatment of quartic invariants at fixed and arbitrary energy
2002 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 43, no 8, 4041-4059 p.Article in journal (Refereed) Published
Abstract [en]

Two-dimensional Hamiltonian systems admitting second invariants which are quartic in the momenta are investigated using the Jacobi geometrization of the dynamics. This approach allows for a unified treatment of invariants at both arbitrary and fixed energy. In the differential geometric picture, the quartic invariant corresponds to the existence of a fourth rank Killing tensor. Expressing the Jacobi metric in terms of a Kähler potential, the integrability condition for the existence of the Killing tensor at fixed energy is a nonlinear equation involving the Kähler potential. At arbitrary energy, further conditions must be imposed which lead to an overdetermined system with isolated solutions. We obtain several new integrable and superintegrable systems in addition to all previously known examples.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-22961 (URN)10.1063/1.1483107 (DOI)
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2017-12-13Bibliographically approved
5. Elastic Stars in General Relativity: I. Foundations and Equilibrium Models
Open this publication in new window or tab >>Elastic Stars in General Relativity: I. Foundations and Equilibrium Models
2003 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 20, no 16, 3613-3648 p.Article in journal (Refereed) Published
Abstract [en]

The aim of this paper is twofold. First, we set up the theory of elastic matter sources within the framework of general relativity in a self-contained manner. The discussion is primarily based on the presentation of Carter and Quintana but also includes new methods and results as well as some modifications that in our opinion make the theory more modern and transparent. For instance, the equations of motion for the matter are shown to take a neat form when expressed in terms of the relativistic Hadamard elasticity tensor. Using this formulation, we obtain simple formulae for the speeds of elastic wave propagation along eigendirections of the pressure tensor. Secondly, we apply the theory to static spherically symmetric configurations using a specific equation of state and consider models either having an elastic crust or core.

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-22962 (URN)10.1088/0264-9381/20/16/307 (DOI)
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2017-12-13Bibliographically approved
6. Elastic Stars in General Relativity: II. Radial Perturbations
Open this publication in new window or tab >>Elastic Stars in General Relativity: II. Radial Perturbations
2004 (English)In: Classical and quantum gravity, ISSN 0264-9381, E-ISSN 1361-6382, Vol. 6, no 21, 1559-1581 p.Article in journal (Refereed) Published
Abstract [en]

We study radial perturbations of general relativistic stars with elastic matter sources. We find that these perturbations are governed by a second-order differential equation which, along with the boundary conditions, defines a Sturm-Liouville-type problem that determines the eigenfrequencies. Although some complications arise compared to the perfect fluid case, leading us to consider a generalization of the standard form of the Sturm-Liouville equation, the main results of Sturm-Liouville theory remain unaltered. As an important consequence we conclude that the mass-radius curve for a one-parameter sequence of regular equilibrium models belonging to some particular equation of state can be used in the same well-known way as in the perfect fluid case, at least if the energy density and the tangential pressure of the background solutions are continuous. In particular, we find that the fundamental mode frequency has a zero for the maximum mass stars of the models with solid crusts considered in paper I of this series

National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-22963 (URN)10.1088/0264-9381/21/6/018 (DOI)
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2017-12-13Bibliographically approved

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