Papers by Yusuf Küçükakça
Astrophysics and Space Science, 2013
Journal of Geometry and Physics, 2009
The objective of this paper is twofold: (a) First the curvature collineations of the Bianchi type... more The objective of this paper is twofold: (a) First the curvature collineations of the Bianchi type V spacetimes are studied using rank argument of curvature matrix. It is found that the rank of the 6 × 6 curvature matrix is 3, 4, 5 or 6 for these spacetimes. In one of the rank 3 cases the Bianchi type V spacetime admits proper curvature collineations which form infinite dimensional Lie algebra. (b) Then the Weyl collineations of the Bianchi type V spacetimes are investigated using rank argument of the Weyl matrix. It is obtained that the rank of the 6 × 6 Weyl matrix for Bianchi type V spacetimes is 0, 4 or 6. It is further shown that these spacetimes do not admit proper Weyl collineations, except in the trivial rank 0 case, which obviously form infinite dimensional Lie algebra. In some special cases it is found that these spacetimes admit Weyl collineations in addition to the Killing vectors, which are in fact proper conformal Killing vectors. The obtained conformal Killing vectors form four-dimensional Lie algebra.
Astrophysics and Space Science, 2012
In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Pal... more In this study, we consider a flat Friedmann-Robertson-Walker (FRW) universe in the context of Palatini f (R) theory of gravity. Using the dynamical equivalence between f (R) gravity and scalar-tensor theories, we construct a point Lagrangian in the flat FRW spacetime. Applying Noether gauge symmetry approach for this f (R) Lagrangian we find out the form of f (R) and the exact solution for cosmic scale factor. It is shown that the resulting form of f (R) yield a powerlaw expansion for the scale factor of the universe.
Journal of Geometry and Physics, 2009
The objective of this paper is twofold: (a) First the curvature collineations of the Bianchi type... more The objective of this paper is twofold: (a) First the curvature collineations of the Bianchi type V spacetimes are studied using rank argument of curvature matrix. It is found that the rank of the 6 × 6 curvature matrix is 3, 4, 5 or 6 for these spacetimes. In one of the rank 3 cases the Bianchi type V spacetime admits proper curvature collineations which form infinite dimensional Lie algebra. (b) Then the Weyl collineations of the Bianchi type V spacetimes are investigated using rank argument of the Weyl matrix. It is obtained that the rank of the 6 × 6 Weyl matrix for Bianchi type V spacetimes is 0, 4 or 6. It is further shown that these spacetimes do not admit proper Weyl collineations, except in the trivial rank 0 case, which obviously form infinite dimensional Lie algebra. In some special cases it is found that these spacetimes admit Weyl collineations in addition to the Killing vectors, which are in fact proper conformal Killing vectors. The obtained conformal Killing vectors form four-dimensional Lie algebra.
Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs spacetimes in scalar-coupled gravity theories
Physical Review D, 2007
We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noe... more We consider some scalar-coupled theories of gravity, including induced gravity, and study the Noether symmetries of Bianchi I, Bianchi III, and Kantowski-Sachs cosmological models for this theory. For various forms of coupling of the scalar field with gravity, some potentials are found in these cosmological models under the assumption that the Lagrangian admits Noether symmetry. The solutions of the field
General Relativity and Gravitation, 2012
Following up on hints of anisotropy in the cosmic microwave background radiation (CMB) data, we i... more Following up on hints of anisotropy in the cosmic microwave background radiation (CMB) data, we investigate locally rotational symmetric (LRS) Bianchi type I spacetimes with non-minimally coupled scalar fields. To single out potentially more interesting solutions, we search for Noether symmetry in this system. We then specialize to the Brans-Dicke (BD) field in such a way that the Lagrangian becomes degenerate (nontrivial) and solve the equations for Noether symmetry and the potential that allows it. Then we find the exact solutions of the equations of motion in terms of three parameters and an arbitrary function. We illustrate with families of examples designed to be generalizations of the well-known power-expansion, exponential expansion and Big Rip models in the Friedmann-Robertson-Walker (FRW) framework. The solutions display surprising variation, a large subset of which features late-time acceleration as is usually ascribed to dark energy (phantom or quintensence), and is consistent with observational data.
Astrophysics and Space Science, 2013
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Papers by Yusuf Küçükakça