Ismail Tarhan

RICCI COLLINEATIONS OF THE BIANCHI TYPES I AND III, AND KANTOWSKI–SACHS SPACETIMES

Ricci collineations of the Bianchi types I and III, and Kantowski–Sachs spacetimes are classified according to their Ricci collineation vector (RCV) field of the form (i)–(iv) one component of ξa(xb) is nonzero, (v)–(x) two components of ξa(xb) are nonzero, and (xi)–(xiv) three components of ξa(xb) are nonzero. Their relation with isometries of the spacetimes is established. In case (v), when det(Rab)=0, some metrics are found under the time transformation, in which some of these metrics are known, and the other ones new. Finally, the family of contracted Ricci collineations (CRC) are presented.

Generation of Bianchi Type V Universes Filled with A Perfect Fluid

Assuming a perfect fluid distribution of matter Bianchi type Vspace-time is considered and using a new generation techniqueit is shown that the field equations are solvable for anyarbitrary cosmic scale function. Solutions for particularforms of cosmic scale functions are obtained, and thegeometrical and physical properties of these solutions discussed.

Some string cosmological models in Bianchi Type I space-time

We obtain some cosmological models that are exact solutions of Einsteins field equations. The metric utilized is Marders metric which is Bianchi Type I and the curvature source is a cloud of strings which are one dimensional objects. Bianchi type cosmological models play an important role in the study of the universe on a scale which anisotropy is not ignored. In this paper we have investigated the effect of cosmic strings on the cosmic microwave background anisotropy. Various physical and geometrical properties of the model are also discussed. The solutions have reported that the cosmic microwave background anisotropy may due to the cosmic strings.

Energy-momentum localization in Marder space-time

Considering the Einstein, Møller, Bergmann-Thomson, Landau-Lifshitz (LL), Papapetrou, Qadir-Sharif and Weinberg’s definitions in general relativity, we find the momentum four-vector of the closed Universe based on Marder space-time. The momentum four-vector (due to matter plus field) is found to be zero. These results support the viewpoints of Banerjee-Sen, Xulu and Aydoġdu-Saltı. Another point is that our study agrees with the previous works of Cooperstock-Israelit, Rosen, Johri et al.

Energy Momentum of Marder Universe in Teleparallel Gravity

Abstract In order to evaluate the energy distribution (due to matter and fields including gravitation) associated with a space-time model of cylindrically-symmetric Marder universe, we consider the Møller, Einstein, Bergmann–Thomson and Landau–Lifshitz energy and momentum definitions in the teleparallel gravity (TG). The energy-momentum distributions are found to be zero. These results are the same as a previous works of Aygün et al., they investigated the same problem in general relativity (GR) by using the Einstein, Møller, Bergmann–Thomson, Landau–Lifshitz (LL), Papapetrou, Qadir–Sharif and Weinberg’s definitions. These results support the viewpoints of Banerjee–Sen, Xulu, Radinschi and Aydoğdu–Saltı. Another point is that our study agree with previous works of Cooperstock–Israelit, Rosen, Johri et al. This paper indicates an important point that these energy-momentum definitions agree with each other not only in general relativity but also in teleparallel gravity. It is also independent of the teleparallel dimensionless coupling constants, which means that it is valid not only in the teleparallel equivalent of general relativity, but also in any teleparallel model.

CONFORMAL COLLINEATIONS IN STRING COSMOLOGY

In this paper, we study the consequences of the existence of conformal collineations (CC) for string cloud in the context of general relativity. Especially, we interest in special conformal collineation (SCC), generated by a special affine conformal collineation (SACC) in the string cloud. Some results on the restrictions imposed by a conformal collineation symmetry in the string cloud are obtained.

CURVATURE INHERITANCE SYMMETRY IN RIEMANNIAN SPACES WITH APPLICATIONS TO STRING CLOUD AND STRING FLUIDS

We study, in this paper, curvature inheritance symmetry (CI), , where α is a scalar function, for string cloud and string fluid in the context of general relativity. Also, we have obtained some result when a proper CI (i.e., α ≠ 0) is also a conformal Killing vector.

On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einsteins simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann–Thomson, Landau–Lifshitz (LL), Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann–Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einsteins universe. Also, several spacetimes are the limiting cases considered here.

ROTATING STRING COSMOLOGIES WITH SCALAR FIELD AND HEAT FLUX

We obtain some cosmological model that are exact solutions of Einstein field equations. The metric utilized is the nonstatic Godel-type cosmological model and the curvature source is a string cloud with scalar field and heat flow. The solutions have nonzero expansion, shear, and rotating. The properties of the solutions are studied and the temperature distribution is also given explicitly.

Møller Energy–Momentum Complex in General Relativity for Higher Dimensional Universes

Using the Moller energy–momentum definition in general relativity (GR) we calculate the total energy–momentum distribution associated with (n+2)-dimensional homogeneous and isotropic model of the universe. It is found that total energy of Moller is vanishing in (n+2) dimensions everywhere but n-momentum components of Moller in (n+2) dimensions are different from zero. Also, we evaluate the static Einstein Universe, FRW universe and de Sitter universe in four dimensions by using (n+2)-type metric, then calculate the Moller energy–momentum distribution of these spacetimes. However, our results are consistent with the results of Banerjee and Sen, Xulu, Radinschi, Vargas, Cooperstock-Israelit, Aygun et al., Rosen, and Johri et al. in four dimensions.