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Slowly rotating fluid balls of Petrov type D
Umeå University, Faculty of Science and Technology, Physics.
Umeå University, Faculty of Science and Technology, Physics.
2007 (English)In: Physical Review D. Particles and fields, ISSN 0556-2821, Vol. 75, no 2, 024013-024026 p.Article in journal (Refereed) Published
Abstract [en]

The second order perturbative field equations for slowly and rigidly rotating perfect fluid balls of Petrov type D are solved numerically. It is found that all the slowly and rigidly rotating perfect fluid balls up to second order, irrespective of Petrov type, may be matched to a possibly nonasymptotically flat stationary axisymmetric vacuum exterior. The Petrov type D interior solutions are characterized by five integration constants, corresponding to density and pressure of the zeroth order configuration, the magnitude of the vorticity, one more second order constant, and an independent spherically symmetric second order small perturbation of the central pressure. A four-dimensional subspace of this five-dimensional parameter space is identified for which the solutions can be matched to an asymptotically flat exterior vacuum region. Hence these solutions are completely determined by the spherical configuration and the magnitude of the vorticity. The physical properties, like equation of state, shape, and speed of sound, are determined for a number of solutions.

Place, publisher, year, edition, pages
2007. Vol. 75, no 2, 024013-024026 p.
URN: urn:nbn:se:umu:diva-2893DOI: 10.1103/PhysRevD.75.024013OAI: diva2:141219
Available from: 2008-01-16 Created: 2008-01-16 Last updated: 2009-06-22Bibliographically approved
In thesis
1. Perturbative Methods in General Relativity
Open this publication in new window or tab >>Perturbative Methods in General Relativity
2008 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Einstein's theory of general relativity is a cornerstone in the process of gaining increased understanding about problems of gravitational nature. It can be applied to problems on the huge length scales of cosmology and as far as we know it does not break down before the Planck scale is approached. Irrespective of scale, a perturbative approach is often a very useful way to reduce the Einstein system to manageable complexity and size.

The projects included in this thesis can be divided into three subcategories. In the first category the keyword is photon-photon scattering. General relativity predicts that scattering can take place on a flat background due to the curvature of space-time caused by the photons themselves. The coupling equations and cross-section are found and a comparison with the corresponding quantum field theoretical results is done to leading order. Moreover, photon-photon scattering due to exchange of virtual electron-positron pairs is considered as an effective field theory in terms of the Heisenberg-Euler Lagrangian resulting in a possible setup for experimental detection of this phenomenon using microwave cavities. The second category of projects is related to cosmology. Here linear perturbations around a flat FRW universe with a cosmological constant are considered and the corresponding temperature variations of the cosmic microwave background radiation are found. Furthermore, cosmological models of Bianchi type V are investigated using a method based on the invariant scheme for classification of metrics by Karlhede. The final category is slowly rotating stars. Here the problem of matching a perfect fluid interior of Petrov type D to an exterior axisymmetric vacuum solution is treated perturbatively up to second order in the rotational parameter.

Place, publisher, year, edition, pages
Umeå: Fysik, 2008. 53 p.
General relativity, perturbation theory, photon-photon scattering, cosmology, FRW models with cosmological constant, Bianchi type V, slowly rotating stars, Hartle formalism
National Category
Physical Sciences
urn:nbn:se:umu:diva-1488 (URN)978-91-7264-493-9 (ISBN)
Public defence
2008-02-07, N420, Naturvetarhuset, Umeå, 14:00
Available from: 2008-01-16 Created: 2008-01-16Bibliographically approved

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