A study of energy conditions in Kantowski–Sachs spacetimes via homothetic vector fields

In this paper, we have studied different energy conditions for some metrics arising from the classification of Kantowski–Sachs spacetimes via homothetic vector fields (HVFs). The homothetic equations for Kantowski–Sachs spacetimes are analyzed using a Maple algorithm which transforms these equations to the reduced involutive form (Rif), giving all possible cases in the form of a tree, known as Rif tree, where the branches of the resulting tree give the potential spacetime metrics which may possess proper HVFs. The set of homothetic equations is integrated for all branches of the Rif tree and the explicit form of HVFs is obtained in ease case. For all the obtained metrics, we have found the bounds for different energy conditions. The stability of these metrics is also discussed.

Conformal and Disformal Structure of 3D Circularly Symmetric Static Metric in f(R) Theory of Gravity

Conformal vector fields are treated as generalization of homothetic vector fields while disformal vector fields are defined through disformal transformations which are generalization of conformal transformations, therefore it is important to study conformal and disformal vector fields. In this paper, conformal and disformal structure of 3D (Three Dimensional) circularly symmetric static metric is discussed in the framework of f(R) theory of gravity. The purpose of this paper is twofold. Firstly, we have found some dust matter solutions of EFEs (Einstein Field Equations) by considering 3D circularly symmetric static metric in the f(R) theory of gravity. Secondly, we have found CKVFs (Conformal Killing Vector Fields) and DKVFs (Disformal Killing Vector Fields) of the obtained solutions by means of some algebraic and direct integration techniques. A metric version of f(R) theory of gravity is used to explore the solutions and dust matter as a source of energy momentum tensor. This study reveals that no proper DVFs exists. Here, DVFs for the solutions under consideration are either HVFs (Homothetic Vector Fields) or KVFs (Killing Vector Fields) in the f(R) theory of gravity. In this study, two cases have been discussed. In the first case, both CKVFs and DKVFs become HVFs with dimension three. In the second case, there exists two subcases. In the first subcase, DKVFs become HVFs with dimension seven. In the second subcase, CKVFs and DKVFs become KVFs having dimension four.

A study of energy conditions in static plane symmetric space–times via homothetic symmetries

The aim of this study is twofold. First, we use a new approach to study the homothetic vector fields (HVFs) of static plane symmetric space–times by an algorithm which we have developed using the Maple platform. The interesting feature of this algorithm is that it provides the most general form of metrics admitting HVFs as compared to those obtained in an earlier study where direct integration techniques were used. Second, the obtained metrics are used in Einstein’s field equations to compute the energy–momentum tensor and it is shown how the parameters involved in the obtained space–time metrics are associated with certain important energy conditions.

Constructing the CKVs of Bianchi III and V spacetimes

We determine the conformal algebra of Bianchi III and Bianchi V spacetimes or, equivalently, we determine all Bianchi III and Bianchi V spacetimes which admit a proper conformal Killing vector (CKV). The algorithm that we use has been developed in [M. Tsamparlis et al.Class. Quantum. Grav. 15, 2909 (1998)] and concerns the computation of the CKVs of decomposable spacetimes. The main point of this method is that a decomposable space admits a CKV if the reduced space admits a gradient homothetic vector, the latter being possible only if the reduced space is flat or a space of constant curvature. We apply this method in a stepwise manner starting from the two-dimensional spacetime which admits an infinite number of CKVs and we construct step by step the Bianchi III and V spacetimes by assuming that CKVs survive as we increase the dimension of the space. We find that there is only one Bianchi III and one Bianchi V spacetime which admit at maximum one proper CKV. In each case, we determine the CKV and the corresponding conformal factor. As a first application in these two spacetimes, we study the kinematics of the comoving observers and the dynamics of the corresponding cosmological fluid. As a second application, we determine in these spacetimes generators of the Lie symmetries of the wave equation.

A note on some Bianchi type II spacetimes and their conformal vector fields in f(R) theory of gravity

The aim of this paper is to find proper conformal vector fields of some Bianchi type II spacetimes in the f[Formula: see text](R[Formula: see text]) theory of gravity using direct integration technique. In this study, seven cases have been discussed. Studying each case in detail, it is shown that the spacetimes under consideration do not admit proper conformal vector fields. Conformal vector fields are either homothetic vector fields or Killing vector fields.

Classification of vacuum classes of plane fronted gravitational waves via proper conformal vector fields in f(R) gravity

In this paper, we have studied proper conformal vector fields of pp-wave space-times in the [Formula: see text] theory of gravity using algebraic and direct integration techniques. From this study, we found that a very special class of pp-waves known as plane fronted gravitational waves (GWs) is a solution in the [Formula: see text] theory of gravity. In order to find proper conformal vector fields, plane GWs are further classified in ten cases. Studying each case in detail it turns out that in two cases proper conformal vector fields exist while in the rest of eight cases, conformal vector fields become homothetic vector fields.

A note on proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in f(R, T) theory of gravity

The purpose of this paper is to find proper homothetic vector fields in plane symmetric perfect fluid static spacetimes in the [Formula: see text] theory of gravity by using direct integration technique. In this study, there exist six cases. Studying each case in detail, we found that in four cases proper homothetic vector fields exist while in the other two cases homothetic vector fields become Killing vector fields.

Classification of static spherically symmetric space-times in f(R) theory of gravity according to their conformal vector fields

A classification of static spherically symmetric space-times in [Formula: see text] theory of gravity according to their conformal vector fields (CVFs) is presented. For this analysis, a direct integration technique is used. This study reveals that for static spherically symmetric space-times in [Formula: see text] theory of gravity, CVFs are just Killing vector fields (KVFs) or homothetic vector fields (HVFs). For this classification, six cases have been discussed out of which there exists only one case for which CVFs become HVFs while in the rest of the cases CVFs become KVFs.