Plane Symmetric Spacetimes Research Articles

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.

Plane Symmetric Solutions in f( $$\mathcal{G}$$ G , T) Gravity

We obtain several exact solutions for a plane symmetric space–time in the framework of a recently constructed f(\(\mathcal{G}\), T) theory of gravity, where f(\(\mathcal{G}\), T) is a generic function of the Gauss–Bonnet invariant G and the trace T of the energy–momentum tensor. To obtain solutions, we consider a power-law f(\(\mathcal{G}\), T) gravity model and analyze the obtained results graphically. Moreover, to justify the method, we reconstruct several well-known cosmological results.

Expanding, shearing and accelerating isotropic plane symmetric universe with conformal Kasner geometry

We construct a model of a universe filled with a perfect fluid with isotropic particle pressure. The anisotropic plane symmetric Kasner spacetime is used as a seed metric and through a conformal mapping a perfect fluid is generated. The model is inhomogeneous, irrotational, shearing and accelerating. For negative time, the universe is expanding, while for positive time, it is collapsing. With the aid of graphical three-dimensional plots, it is established that the density and pressure hypersurfaces are smooth and singularity free. Additionally, the sound-speed index is computed and the fluid obeys the causality criterion. The non-static exact solution found may prove useful in the study of gravitational waves.

Correction to the conservation laws in plane symmetric gravitational wave-like spacetimes

This paper discusses the approximate Noether symmetries of the action of plane symmetric spacetime. A time-dependent conformal factor is introduced in the plane symmetric metric in such a way so as to obtain the same number of Noether symmetries as for the exact plane symmetric spacetime. The corresponding approximate conservation is obtained to discuss the conservation laws of the energy and momentum during the formation of gravitational wave.

Homothetic Ricci collineations in non-static plane symmetric spacetimes with perfect fluid matter

In this paper, we investigate homothetic Ricci collineations (HRCs) for non-static plane symmetric spacetimes. The source of the energy–momentum tensor is assumed to be a perfect fluid. Both degenerate as well as non-degenerate cases are considered and the HRC equations are solved in different cases. It is concluded that these spacetimes may possess 6, 7, 8, 10 or 11 HRCs in non-degenerate case, while they admit seven or infinite number of HRCs for degenerate Ricci tensor.

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.

Colliding scalar pulses in the Einstein-Gauss-Bonnet gravity

We numerically investigated how the nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms, with a model of colliding scalar pulses in plane-symmetric space-time. We observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude depends on αGB. The normal corrections (αGB > 0) work for avoiding the appearance of singularity, although it is inevitable.

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.

Classification of Variational Conservation Laws of General Plane Symmetric Spacetimes

In this article we discuss Noether conservation laws admitted by a Lagrangian of a test particle moving in the field of a general plane symmetric non-static spacetime metric. In this context, we first present a general solution representing a Noether symmetry vector subject to differential constraints satisfied by the general plane symmetric non-static metric. We then use a class of plane symmetric non-static metrics obtained by Feroze et al. and discuss, in each case, Noether conservation laws in comparison with Killing symmetries.

Nonlinear dynamics in the Einstein-Gauss-Bonnet gravity

We numerically investigated how the nonlinear dynamics depends on the dimensionality and on the higher-order curvature corrections in the form of Gauss-Bonnet (GB) terms. We especially monitored the processes of appearances of a singularity (or black hole) in two models: (i) a perturbed wormhole throat in spherically symmetric space-time, and (ii) colliding scalar pulses in plane-symmetric space-time. We used a dual-null formulation for evolving the field equations, which enables us to locate the trapping horizons directly, and also enables us to follow close to the large-curvature region due to its causal integrating scheme. We observed that the fate of a perturbed wormhole is either a black hole or an expanding throat depending on the total energy of the structure, and its threshold depends on the coupling constant of the GB terms ($\alpha_{\rm GB}$). We also observed that a collision of large scalar pulses will produce a large-curvature region, of which the magnitude also depends on $\alpha_{\rm GB}$. For both models, the normal corrections ($\alpha_{\rm GB}>0$) work for avoiding the appearance of singularity, although it is inevitable. We also found that in the critical situation for forming a black hole, the existence of the trapped region in the Einstein-GB gravity does not directly indicate the formation of a black hole.

Plane Symmetric Anisotropic Dark Energy Cosmological Model in the Bimetric Theory of Gravitation

The plane symmetric space-times with anisotropic dark energy and with constant deceleration parameter have been derived by solving the Rosen's field equations in the Bimetric theory of gravitation. We explored both models in power law as well as in exponential law. In power law, the model attains both phases accelerating as well as decelerating in the expansion with anisotropic fluid, which is in the form of dark energy, and there is no chance of real matter in this power law. In exponential law, the model is dust, isotropized in nature with constant acceleration in the expansion. Further, other geometrical and physical aspects of the models are also studied.

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.

Plane Symmetric Cosmological Model with Quark and Strange Quark Matter in f (R, T) Theory of Gravity

We studied plane symmetric cosmological model in the presence of quark and strange quark matter with the help of f(R,T) theory. To decipher solutions of Plane symmetric space-time, we used power law relation between scale factor and deceleration parameter. We considered the special law of variation of Hubble's parameter proposed by Berman (Nuovo Cimento B 74, 182, 1983) which yields constant deceleration parameter. We also discussed the physical behavior of the solutions by using some physical parameters.

Geometrical/Physical Interpretation of the Conserved Quantities Corresponding to Noether Symmetries of Plane Symmetric Space-Times

The aim of this paper is to give the geometrical/physical interpretation of the conserved quantities corresponding to each Noether symmetry of the geodetic Lagrangian of plane symmetric space-times. For this purpose, we present a complete list of plane symmetric nonstatic space-times along with the generators of all Noether symmetries of the geodetic Lagrangian. Additionally, the structure constants of the associated Lie algebras, the Riemann curvature tensors, and the energy-momentum tensors are obtained for each case. It is worth mentioning that the list contains all classes of solutions that have been obtained earlier during the classification of plane symmetric space-times by isometries and homotheties.