Plane Symmetric Static Spacetimes Research Articles

Classification of static plane symmetric spacetime according to their self similar vector fields

Abstract This article discusses the use of self-similar symmetry to analyze static plane symmetric spacetime. A computer algorithm is employed to convert the symmetry equations, resulting in a tree structure known as a Riff tree, which is utilized for analyzing the aforementioned symmetry within the specified spacetime. The tree comprises several pivots and branches, with the pivots being subject to specific differential conditions on the metric functions. Furthermore, explicit formulas for the metrics and their corresponding self-similar vector fields (SSVFs) are derived by solving the set of equations using these constraints. Additionally, this work investigates the bounds for certain energy conditions as well as the kinematic variables.

Ricci solitons on anisotropic fluid spacetime in f(R, T)-gravity

In this paper we study the behaviour of anisotropic fluid spacetimes in f(R, T)-gravity for admitting Ricci Soliton. We obtain the form of tangential pressure of the fluid for steady, shrinking and expanding Ricci soliton when Ricci soliton vector field becomes a Killing vector field. Modified Poisson and Liouville equations are derived from the Ricci soliton equation in f(R, T)-gravity having anisotropic fluid. Also harmonic significance of Ricci soliton on anisotropic fluid spacetime in f(R, T)-gravity with a harmonic potential function is derived. We derive field equations for perfect fluid plane symmetric static spacetime and obtain their solutions. For each solution we then obtain Ricci soliton vector fields. We observe that such spacetimes admit expanding, shrinking or steady Ricci solitons. All the obtained solitons are trivial in nature. When these Ricci soliton vector fields become Killing vector fields then our results are in full agreement with the theorems deduced from our study.

Symmetries of the Energy–Momentum Tensor for Static Plane Symmetric Spacetimes

This article explores matter collineations (MCs) of static plane-symmetric spacetimes, considering the stress–energy tensor in its contravariant and mixed forms. We solve the MC equations in two cases: when the energy–momentum tensor is nondegenerate and degenerate. For the case of a degenerate energy–momentum tensor, we employ a direct integration technique to solve the MC equations, which leads to an infinite-dimensional Lie algebra. On the other hand, when considering the nondegenerate energy–momentum tensor, the contravariant form results in a finite-dimensional Lie algebra with dimensions of either 4 or 10. However, in the case of the mixed form of the energy–momentum tensor, the dimension of the Lie algebra is infinite. Moreover, the obtained MCs are compared with those already found for covariant stress–energy.

A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

A note on concircular vector fields of static plane symmetric perfect fluid spacetimes in f(T) theory of gravity

A note on classification of dust static plane symmetric space-times via proper curvature collineations in f(R) gravity

In this paper, we classify dust static plane symmetric (SPS) space-times via proper curvature collineations (CCs) in the [Formula: see text] gravity using the rank of [Formula: see text] Riemann matrix and direct integration technique. Classifying the above mentioned space-times, we find that there arise six cases corresponding to specific values of the function [Formula: see text]. Inspecting all the cases, we reach at the fact that there exist two cases where the space-times admit proper CCs which form an infinite dimensional vector space (IDVS). In rest of the four cases, the space-time becomes either flat or CCs become the killing vector fields (KVFs).

A note on classification of static plane symmetric perfect fluid space-times via proper conformal vector fields in f(G) theory of gravity

In the [Formula: see text] theory of gravity, we classify static plane symmetric perfect fluid space-times via proper conformal vector fields (CVFs) using algebraic and direct integration approaches. During this classification, we found eight cases. Studying each case in detail, we found that the dimensions of CVFs are 4, 5, 6 or 15. In the cases when the space-time admits 15 independent CVFs it becomes conformally flat.

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.

Homothetic matter collineations of static plane symmetric spacetimes

In this paper, we present a complete classification of static plane symmetric spacetimes via their homothetic symmetries of the energy–momentum tensor, known as homothetic matter collineations (HMCs). The HMC equations for these spacetimes are derived and then solved by considering the degeneracy and non-degeneracy of the energy–momentum tensor. In the former case, we have obtained 6, 11 and infinite number of HMCs, while in the latter case, the solution of HMC equations yields 6-, 7-, 8-, 10- and 11-dimensional algebra of HMCs. The obtained HMCs generate some differential constraints involving the components of the energy–momentum tensor. Some examples of static plane symmetric spacetime metrics satisfying these constraints are provided and the physical interpretations of these metrics are discussed.

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.

Analysis of Einstein Field Equations of Static Plane Symmetric Space-Time in General Relativity via Lie Approach

In this study, Einstein field equations of static plane symmetric space-time is discussed by means of Lie approach. Lie point symmetries are computed for the considered equations. Moreover, one dimensional conjugacy classes for symmetry algebra are reported. Additionally, similarity variables are derived which are further utilized to find the solutions for parameters $A$ and $B$ of the considered space-time. Both linearly independent and dependent relationships between the unknown parameters $A$ and $B$ are observed for different cases. At the end, some well-known solutions are presented.

The Second-Order Correction to the Energy and Momentum in Plane Symmetric Gravitational Waves Like Spacetimes

This research provides second-order approximate Noether symmetries of geodetic Lagrangian of time-conformal plane symmetric spacetime. A time-conformal factor is of the form e ϵ f ( t ) which perturbs the plane symmetric static spacetime, where ϵ is small a positive parameter that produces perturbation in the spacetime. By considering the perturbation up to second-order in ϵ in plane symmetric spacetime, we find the second order approximate Noether symmetries for the corresponding Lagrangian. Using Noether theorem, the corresponding second order approximate conservation laws are investigated for plane symmetric gravitational waves like spacetimes. This technique tells about the energy content of the gravitational waves.

Dust static plane symmetric solutions and their conformal vector fields in f(R) theory of gravity

We first find the dust solutions of static plane symmetric spacetimes in the theory of f(R) gravity. Then using the direct integration technique on the solutions obtained, we deduce the conformal vector fields. This is performed in the context of f(R) theory of gravity. There exist six cases. Out of these, in five cases the spacetimes become conformally flat and admit 15 conformal vector fields, whereas in the sixth case, conformal vector fields become Killing vector fields.

Conformal Collineations of the Ricci and Energy–Momentum Tensors in Static Plane Symmetric Space–Times

We provide a complete classification of static plane symmetric space–times according to conformal Ricci collineations (CRCs) and conformal matter collineations (CMCs) in both the degenerate and nondegenerate cases. In the case of a nondegenerate Ricci tensor, we find a general form of the vector field generating CRCs in terms of unknown functions of t and x subject to some integrability conditions. We then solve the integrability conditions in different cases depending upon the nature of the Ricci tensor and conclude that the static plane symmetric space–times have a 7-, 10- or 15-dimensional Lie algebra of CRCs. Moreover, we find that these space–times admit an infinite number of CRCs if the Ricci tensor is degenerate. We use a similar procedure to study CMCs in the case of a degenerate or nondegenerate matter tensor. We obtain the exact form of some static plane symmetric space–time metrics that admit nontrivial CRCs and CMCs. Finally, we present some physical applications of our obtained results by considering a perfect fluid as a source of the energy–momentum tensor.

Conformal collineations of the Ricci and energy-momentum tensors in static plane symmetric space-times

Проведена полная классификация статических плоских симметричных пространств-времен по их конформным коллинеациям Риччи и конформным коллинеациям материи как в вырожденном, так и в невырожденном случаях. Для невырожденного тензора Риччи найден общий вид векторного поля, генерирующего конформные коллинеации Риччи, в терминах неизвестных функций от $t$ и $x$, которые подчиняются некоторым условиям интегрируемости. Приведено решение этих условий в различных случаях, зависящих от природы тензора Риччи, и сделан вывод о том, что статическое плоское пространство-время обладает семи-, десяти- или пятнадцатимерной алгеброй Ли конформных коллинеаций Риччи. Кроме того, обнаружено, что если тензор Риччи вырожден, то такое пространство-время допускает бесконечное число конформных коллинеаций Риччи. Аналогичная процедура применяется для конформных коллинеаций материи в случае вырожденного или невырожденного тензора материи. Получен точный вид некоторой метрики статического плоского пространства-времени, допускающей нетривиальные конформные коллинеации Риччи и конформные коллинеации материи. Представлены некоторые физические применения полученных результатов: в качестве источника тензора энергии-импульса рассмотрена идеальная жидкость.

Proper Curvature Collineations of Plane Symmetric Static Spacetime in F(R) Theory of Gravity

The purpose of this paper is to study the proper curvature collineations of plane symmetric static spacetime in f(R) theory of gravity. We have taken the metrics of both constant and non-constant curvature and formulated the curvature vector fields by using vanishing Lie derivative and direct integration technique. Here, the solutions of the Einstein’s field equations (EFEs) for both cases involve inverse curvature terms which may cause an increase in gravity that justifies the accelerated expansion of the universe. It turns out that curvature collineations become Killing vector fields and therefore, proper curvature collineations do not exists in both the cases.

Plane Symmetric Solutions in f(G) Gravity

The purpose of this document is to investigate the universe in f(G) gravity. A wgeneral static plane symmetric space-time is chosen and exact solutions are explored using a viable f(G) gravity model. In particular, power and exponential law solutions are discussed. In addition, the physical relevance of the solutions with Taub’s metric and anti-deSitter space-time is shown. Graphical analysis of energy density and pressure of the universe is done to substantiate the study.

Proper Teleparallel Homothetic Vector Fields in General Cylindrically Symmetric Space-Times in Teleparallel Theory of Gravitation Using Diagonal Tetrads

In this paper we consider the most general form of non-static cylindrically symmetric space-times in order to study proper teleparallel homothetic vector fields using the direct integration technique and diagonal tetrads. This study also covers static cylindrically symmetric, Bianchi type I, non-static and static plane symmetric space-times as well. Here, we will only discuss the cases which do not fall in the category of static cylindrically symmetric, Bianchi type I, non-static and static plane symmetric space-times. From the above study we show that very special classes of the above space-times yield 6, 7 and 8 teleparallel homothetic vector fields with non-zero torsion.

Proper conformal Killing vectors in static plane symmetric space–times

Conformal Killing vectors (CKVs) in static plane symmetric space–times were recently studied by Saifullah and Yazdan, who concluded by remarking that static plane symmetric space–times do not admit any proper CKV except in the case where these space–times are conformally flat. We present some non-conformally flat static plane symmetric space–time metrics admitting proper CKVs. For these space–times, we also investigate a special type of CKVs, known as inheriting CKVs.

Propagation of Scalar Fields in a Plane Symmetric Spacetime

The present article deals with solutions for a minimally coupled scalar field propagating in a static plane symmetric spacetime. The considered metric describes the curvature outside a massive infinity plate and exhibits an intrinsic naked singularity (a singular plane) that makes the accessible universe finite in extension. This solution can be interpreted as describing the spacetime of static domain walls. In this context, a first solution is given in terms of zero order Bessel functions of the first and second kind and presents a stationary pattern which is interpreted as a result of the reflection of the scalar waves at the singular plane. This is an evidence, at least for the massless scalar field, of an old interpretation given by Amundsen and Gron regarding the behaviour of test particles near the singularity. A second solution is obtained in the limit of a weak gravitational field which is valid only far from the singularity. In this limit, it was possible to find out an analytic solution for the scalar field in terms of the Kummer and Tricomi confluent hypergeometric functions.

Classification of static plane symmetric spacetime via Noether gauge symmetries

In this paper, general static plane symmetric spacetime is classified with respect to Noether operators. For this purpose, Noether theorem is used which yields a set of linear partial differential equations (PDEs) with unknown radial functions [Formula: see text], [Formula: see text] and [Formula: see text]. Further, these PDEs are solved by taking different possibilities of radial functions. In the first case, all radial functions are considered same, while two functions are taken proportional to each other in second case, which further discussed by taking four different relationships between [Formula: see text], [Formula: see text] and [Formula: see text]. For all cases, different forms of unknown functions of radial factor [Formula: see text] are reported for nontrivial Noether operators with non-zero gauge term. At the end, a list of conserved quantities for each Noether operator Tables 1–4 is presented.