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Elastic Stars in General Relativity: II. Radial Perturbations
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
Stockholm University, Faculty of Science, Department of Physics.
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

Place, publisher, year, edition, pages
2004. Vol. 6, no 21, 1559-1581 p.
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-22963DOI: 10.1088/0264-9381/21/6/018OAI: oai:DiVA.org:su-22963DiVA: diva2:189816
Available from: 2003-09-25 Created: 2003-09-25 Last updated: 2017-12-13Bibliographically approved
In thesis
1. Stellar Models in General Relativity
Open this publication in new window or tab >>Stellar Models in General Relativity
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
General relativity, compact objects, neutron stars
National Category
Physical Sciences
Identifiers
urn:nbn:se:su:diva-13 (URN)91-7265-746-4 (ISBN)
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

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