Department of Mathematics

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Browsing Department of Mathematics by Subject "04.20.Jb"

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    On a particular type of product manifolds and shear-free cosmological models
    (Institute of Physics Publishing, 2011) Gürses M.; Plaue, M.; Scherfner, M.
    Shear-free flows or observer fields are important objects of study in general relativity; stationary or rigid observers are important examples of shear-free reference frames. In this paper, we introduce a geometric structure based on a local coordinate expression of metrics admitting a shear-free reference frame. Furthermore, we investigate a large sub-class of these models ('tilted' warped products) that includes the Robertson-Walker spacetime, the Gödel spacetime and other models of Gödel type. We present a novel example of a rotating and expanding cosmological model that is contained in this class. Finally, we describe the geodesic barotropic perfect fluid solutions. © 2011 IOP Publishing Ltd.
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    Some exact solutions of all f (R μν) theories in three dimensions
    (American Physical Society, 2012) Gürses, M.; Şişman, T. Ç.; Tekin, B.
    We find constant scalar curvature Type-N and Type-D solutions in all higher curvature gravity theories with actions of the form f(R μν) that are built on the Ricci tensor, but not on its derivatives. In our construction, these higher derivative theories inherit some of the previously studied solutions of the cosmological topologically massive gravity and the new massive gravity field equations, once the parameters of the theories are adjusted. Besides the generic higher curvature theory, we have considered in some detail the examples of the quadratic curvature theory, the cubic curvature theory, and the Born-Infeld extension of the new massive gravity. © 2012 American Physical Society.