Tez özetleri Astronomi ve Uzay Bilimleri Anabilim Dalı 2

Shear-Free Cosmıc Fluıd Conjecture ın Hıgh Order Curvature Gravıty
In this thesis, we have investigated whether or not there is a counterpart of the relativistic shear-free perfect fluid conjecture within the context of F(R)-gravity, F(G)-gravity and braneworld theories. In F(R) and F(G)-gravities by adopting a metric based approach and making use of tetrad equations, extended to these theories we have considered three spatially homogeneous metrics in order to investigate the existence of simultaneously rotating and expanding solutions of the F(R)-gravity and F(G)-gravity field equations with shear-free perfect fluids as sources. We have shown that in F(R)-gravity the Gödel type expanding universe, as well as a rotating Bianchi-type II spacetime allow no such solutions of the field equations of this modified gravity. On the other hand, we have found that there exist two types of F(R) models in which a shear-free Bianchi-type IX universe can expand and rotate at the same time. The matter content of this universe is described by a perfect fluid having positive or negative pressure, depending on the type of F(R) model and on the cosmological constant; in the particular case of a vanishing cosmological constant we have found that the universe is filled with a pure radiation. Whatsoever the cases, the universe exhibits always coasting anisotropic expansions along three spatial directions evolving like a flat Milne universe, and has a vorticity inversely proportional to cosmic time. A further result is that, due to the nonvanishing of the gravito-magnetic part of the Weyl tensor, this model allows for gravitational waves. Our solution constitutes one more example giving support to that in F(R)-gravity there is no counterpart of the general relativistic shear-free conjecture.
In F(G)-gravity, we have found that an expanding version of the stationary Gödel metric is not admitted as solution of field equations. By contrast a class of a further generalized form of the Gödel metric could be allowed as solution of the full set of tetrad equations without leading to any inconsistencies. However, due to the functional complexity of the time dependence of the scale factor the reconstruction of a F(G) model is avoided. Such a situation has been also encountered in rotating Bianchi-tip IX model.
In braneworld models, we have used the consistency analysis approach of the covariant constraint equations and have considered two special cases: for the pure braneworld in the acceleration-free pure-Coulombien case we have shown that the conjecture is true while for the F(R)-braneworld with induced gravity and pure braneworld in the acceleration-free case there may be situations where a shear-free perfect fluid could have simultaneous rotation and expansion.
  

KARABUL Yaşar

Danışman : Yard. Doç. Dr. Lidya SUSAM

Anabilim Dalı : Fizik

Programı : Nükleer Fizik

Mezuniyet Yılı : 2014

Tez Savunma Jürisi : Yrd. Doç. Lidya Susam

Prof. Dr. Baki Akkuş

Prof. Dr. Yeşim Öktem

Doç. Dr. R. Burcu Çakırlı

Yrd. Doç. Dr. H. Birtan Kavanoz