This paper aims to investigate Conformal Vector Fields (CVFs) of Bianchi type-I spacetimes. A set of 10-coupled Partial Differential Equations (PDEs) is obtained from the conformal Killing equations. These equations are solved by using direct integration techniques to explore the components of CVFs. Utilizing these components, we get a system of three integrability conditions. Finally, we achieve CVFs along with conformal factors for unique possibilities of unknown metric functions from the solution of these conditions. From our results, it is examined that Bianchi type-I spacetimes admit five or fifteen CVFs for specific choices of metric functions.
In this paper, Bianchi type I space-times in the [Formula: see text] theory of gravity are classified via conformal vector fields using algebraic and direct integration techniques. In this classification, we show that the conformal vector fields are of dimension four, five, six or fifteen. Additionally, we found that non-conformally flat Bianchi type I space-times admit conformal vector fields of dimension four, five or six. In the case of conformally flat or flat space-times, the dimension of the conformal vector fields is fifteen.
The purpose of this paper is to find conformal vector fields of some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes in the [Formula: see text] theory of gravity using direct integration technique. In this study, there exist only eight cases. Studying each case in detail, we found that in two cases proper conformal vector fields exist while in the rest of the cases, conformal vector fields become Killing vector fields. The dimension of conformal vector fields is either 4 or 6.
In this paper, homothetic vector fields of a spatially homogenous Bianchi type-I cosmological model have been evaluated based on Lyra geometry. Further, we investigate the equation of state in cases when a displacement vector [Formula: see text] is a function of t and when it is constant. We give a comparison between the obtained results, using Lyra geometry, and those obtained previously in the context of general relativity, based on Riemannian geometry.
Barber's second self creation theory with perfect fluid source for an LRS Bianchi type-I metric is considered using deceleration parameter to be constant where the metric potentials are taken as functions of x and t. In particular, some exact solutions have also been obtained for the vacuum universe, Zel'dovich universe and radiation universe. Some physical properties of the models are also discussed.
A note on some perfect fluid Kantowski–Sachs and Bianchi type III spacetimes and their conformal vector fields in f(R) theory of gravity