Perfect Fluid Distribution Research Articles

New classes of charged 4D EGB spacetimes with vanishing Weyl curvature

AbstractThe configuration of a perfect fluid distribution in an electric field under the influence of higher curvature geometric effects introduced through the Gauss–Bonnet invariants is studied in the 4 dimensional Glavan–Lin gravity formulation. It is found that whereas a constant spatially directed gravitational potential gives isothermal behaviour in the standard theory, this is not the case when extra curvature is present in general. A physically viable stellar model is constructed by assuming the Finch–Skea potential. The geometry and electrodynamics are well behaved being regular throughout the distribution including the centre. The model passes stability tests such as the Chandrasekar adiabatic stability criterion and causality. Additionally all energy conditions are satisfied within the star. We compare the performance of the model with its Einstein counterpart and observe that the higher curvature exerts a notable influence on all the physical properties of the star.

A new perspective on gravitational collapse: a comprehensive analysis using Θ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Theta $$\\end{document} parametrization

In this article, we have studied some new facets of gravitational collapse, beyond conventional notions of black holes, and naked singularities. The present work is focused on the unresolved problems of theoretical physics concerning the final fate of the gravitational collapse of any massive star. By generalizing the foundational work of Oppenheimer and Snyder (Phys Rev 56:455, 1939), we have considered the homogeneous gravitational collapsing system filled with perfect fluid distributions (devoid of dust fluid) within the framework of GR theory. The article investigates a homogeneous gravitational collapsing system using a parametrization scheme for the expansion-scalar (Θ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\Theta )$$\\end{document} and determining the exact solution of field equations. Further, by employing the known Darmois–Israel boundary condition, we have discussed the solution in more detail, and the model’s physical and geometrical quantities are obtained in terms of stellar mass (M), making it crucial for astrophysical applications. To assess the astrophysical viability of our model, we consider a massive star-β\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\beta $$\\end{document}Canis Majoris and throughout this study we have presented a detailed numerical and graphical analysis of our model. The analysis of singularities in the models is conducted through the examination of the apparent horizon. Our findings demonstrate that the star continues to collapse indefinitely in co-moving time, ultimately leading to a space-time singularity-this represents a case of continuous gravitational collapse. We propose that this scenario describes an “Eternal Collapsing Object,” which may be treated as a “mathematical black hole without any finite equilibrium state.” Our presented models undergo rigorous physical tests to ensure their regularity, causality, and stability, and to satisfy the necessary energy conditions.

Minimal Einstein-Aether theory

We show that there is a phenomenologically and theoretically consistent limit of the generic Einstein-Aether theory in which the Einstein-Aether field equations reduce to Einstein field equations with a perfect fluid distribution sourced by the aether field. This limit is obtained by taking three of the coupling constants of the theory to be zero but keeping the expansion coupling constant to be nonzero. We then consider the further reduction of this limited version of Einstein-Aether theory by taking the expansion of the aether field to be constant (possibly zero), and thereby we introduce the Minimal Einstein-Aether theory that supports the Einstein metrics as solutions with a reduced cosmological constant. The square of the expansion of the unit-timelike aether field shifts the bare cosmological constant and thus provides, via local Lorentz symmetry breaking inherent in the Einstein-Aether theories, a novel mechanism for reconciling the observed, small cosmological constant (or dark energy) with the large theoretical prediction coming from quantum field theories. The crucial point here is that minimal Einstein-Aether theory does not modify the well-tested aspects of General Relativity such as solar system tests and black hole physics including gravitational waves.

Non-static plane symmetric perfect fluid solutions and Killing symmetries in f(R, T) gravity

In this paper, the non-static solutions for perfect fluid distribution with plane symmetry in f(R, T) gravitational theory are obtained. Firstly, using the Lie symmetries, symmetry reductions are performed for considered vector fields to reduce the number of independent variables. Then, corresponding to each reduction, exact solutions are obtained. Killing vectors lead to different conserved quantities. Therefore, we figure out the Killing vector fields corresponding to all derived solutions. The derived solutions are further studied and it is observed that all of the obtained spacetimes, at least admit to the minimal symmetry group which consists of ∂ y , ∂ z and −z∂ y + y∂ z . The obtained metrics, admit to 3, 4, 6, and 10, Killing vector fields. Conservation of linear momentum in the direction of y and z, and angular momentum along the x axis is provided by all derived solutions.

A study of compact stars within Rastall gravity

In this paper, we construct the exact interior solutions for compact stellar objects for perfect fluid distribution in phantom region in the framework of a non-conserved theory, i.e. Rastall gravity (RG). Under these circumstances, we develop the Einstein field equations (EFEs) for spherically symmetric metric using general forms of metric potentials, [Formula: see text] and [Formula: see text], here [Formula: see text] and [Formula: see text]. By matching of interior and exterior regions of the metric, we obtain the values of unknown constants of our considering model which helps to sketch the nature of important physical quantities like density, pressure, energy conditions, and stability. Finally, our obtained results lead us to conclude that our solutions are well behaved and physically viable for the specific choices of model parameters for two different stars (Vela X-1 and 4U1820-30).

Bianchi Type-VIII Inflationary Cosmological Models with Flat Potential and Stiff perfect Fluid Distribution in General Relativity

The objective of this paper is to investigate the behaviour of Bianchi Type-VIII Inflationary Cosmological Models with Flat Potential for Stiff Fluid Distribution. To find the solution of thes models we consider that the expansion theta is proportional to the shear sigma, which leads to B = An and potential V (phi ) as a constant. The behaviour of these models from physical and geometrical aspects are also discussed.

FLRW Universe in f(R,Lm) Gravity with Equation of State Parameter

Available observational data regarding current cosmological characteristics suggest that the universe is, to a large extent, both isotropic and homogeneous on a large scale. In this study, our objective is to analyze the Friedmann-Lemaitre-Robertson-Walker (FLRW) space-time using a perfect fluid distribution. We specifically investigate the framework of f(R, Lm) gravity within certain constraints. To accomplish this, we concentrate on a specific nonlinear f(R, Lm) model, represented by f(R, Lm) = R/2 + Lαm. The field equations are solved using the equation of state parameter of the form of the Chevallier-Polarski-Linder (CPL) parameterization. The deceleration parameter study finds an accelerating universe at late times. The transition redshift is found to be ztr = 0.89 ± 0.25. Also, we discussed the physical and geometrical properties of the model.

Can Charged Stars be Singularity‐Free?

AbstractWhile the configuration of a static spherically symmetric distribution of perfect fluid in an electric field has received extensive attention in the literature, only a few works have investigated the conformally flat case. The model exhibits a remarkable property being regular or singularity free is proposed. This is unexpected given that Coulombic repulsion opposes the collapse of a star to the center generally making the center unreachable. The conformally flat geometry thus enables the approach to the center of a charged star as shown in our model. Presently there is no known reported exact model that satisfies all the elementary requirements for physical acceptability. Some reported models that have claimed to be physically reliable have been shown to be deficient. The conditions for the existence of physically relevant models and show that exact solutions satisfying the conditions exist is investigated. Then a model satisfying all the requirements with isotropic particle pressure graphically for a carefully chosen parameter space is exhibited. The model admits a barotropic equation of state. The interior spacetime is successfully matched to the exterior Reissner‐Nordstrom metric. The causality criterion as well as the adiabatic stability lower bound of Chandrasekar are shown to hold. The energy conditions are also valid within the stellar radius. Other interesting models are considered.

Self-Similar Solutions of a Bianchi Type-III Model with a Perfect Fluid and Cosmic String Cloud in Riemannian Geometry

A Bianchi type-III cosmological model with self-similarity symmetry is investigated in cases with perfect fluid distribution and a cosmic string cloud. We show that this model admits a non-trivial homothetic vector field which possess non-null homothetic bivectors. This homothetic vector field is not parallel to its source vector (current vector). We discussed cases where the homothetic vector is either orthogonal or parallel to the 4-velocity of a fluid element. We solved Einstein’s field equations without making any assumptions on the geometry of space-time, only assuming that it admits self-similarity symmetry. We obtained new exact self-similar solutions for the Bianchi type-III model. We show that all obtained solutions are shear, and space-time is shear free in only the case where the homothetic vector field is parallel to the 4-velocity vector. The kinematical and physical properties of the obtained solutions are discussed.

Evolution of gravitational waves in non-minimal coupling between geometry and matter theories of gravity

We consider some specific models of non-minimal matter–geometry coupling theories and investigate the propagation of the gravitational waves in them. Extracting the temporal evolution of the gravitational wave equation within the framework of a flat FRW universe with a perfect fluid distribution, we analyze the waveforms traveling during the time. We find that while both the amplitude and frequency of the GWs decay with time in all considered models, the rate of reduction is highly sensitive to the values of the equation of state parameter and input parameters of the considered models.

ANISOTROPIC TILTED SPHERICAL FALSE VACUUM MODEL

In this paper, a tilted spherically symmetric cosmological model with perfect fluid distribution along with heat conduction has been considered. To get a generalized solution, I have assumed the model to be False Vacuum (i.e. ), where p being the isotropic pressure and is the matter density of the fluid. The various physical properties of the model are also discussion as the concluding remark

Complexity-free solution generated by gravitational decoupling for anisotropic self-gravitating star in symmetric teleparallel f(Q)-gravity theory

In this work, we attempt to find an anisotropic solution for a compact star generated by gravitational decoupling in f(Q)-gravity theory having a null complexity factor. To do this, we initially derive the complexity factor condition in f(Q) gravity theory using the definition given by Herrera (Phys Rev D 97:044010, 2018) and then derived a bridge equation between gravitational potentials by assuming complexity factor to be zero (Contreras and Stuchlik in Eur Phys J C 82:706, 2022). Next, we obtain two systems of equations using the complete geometric deformation (CGD) approach. The first system of equations is assumed to be an isotropic system in f(Q)-gravity whose isotropic condition is similar to GR while the second system is dependent on deformation functions. The solution of the first system is obtained by Buchdahl’s spacetime geometry while the governing equations for the second system are solved through the mimic constraint approach along with vanishing complexity condition. The novelty of our work is to generalize the perfect fluid solution into an anisotropic domain in f(Q)-gravity theory with zero complexity for the first time. We present the solution’s analysis to test its physical viability. We exhibit that the existence of pressure anisotropy due to gravitational within the self-gravitating bounded object plays a vital role to stabilize the f(Q) gravity system. In addition, we show that the constant involved in the solution controls the direction of energy flow between the perfect fluid and generic fluid matter distributions.

SOME BIANCHI TYPE III STRING COSMOLOGICAL MODELS FOR PERFECT FLUID DISTRIBUTION IN GENERAL RELATIVITY WITH AN ALTERNATE APPROACH

Some Bianchi type III string cosmological models for perfect fluid distribution with an alternate approach are discussed, assuming a condition between energy density and string tension density. We have also assumed a relation between metric potentials to get deterministic solution. The physical and geometrical aspects of the models are also discussed

First Integrals of Shear-Free Fluids and Complexity

A single master equation governs the behaviour of shear-free neutral perfect fluid distributions arising in gravity theories. In this paper, we study the integrability of find new solutions, and generate a new first integral. The first integral is subject to an integrability condition which is an integral equation which restricts the function We find that the integrability condition can be written as a third order differential equation whose solution can be expressed in terms of elementary functions and elliptic integrals. The solution of the integrability condition is generally given parametrically. A particular form of which corresponds to repeated roots of a cubic equation is given explicitly, which is a new result. Our investigation demonstrates that complexity of a self-gravitating shear-free fluid is related to the existence of a first integral, and this may be extendable to general matter distributions.

On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

On new symmetries and exact solutions of Einstein’s field equation for perfect fluid distribution

Bianchi - III inflationary universe for perfect fluid distribution using Cosmological constant in general relativity

In this study Bianchi-III universe for perfect fluid under effect of the cosmological constant is investigated. The complicated system of field’s equations are resolved in the existence of conservation condition of energy-momentum and a relativistic relation among metric potential is assumed i.e. b = c k . here k ` 1 is a constant. The dynamical features of the constructed model are also pointed

Energy conditions in non‐minimally coupled f(R, T) gravity

In today's scenario, going beyond Einstein's theory of gravity leads us to some more complete and modified gravity theories. One of them is the f(R, T) gravity in which R is the Ricci scalar, and T is the trace of the energy‐momentum tensor. Using a well‐motivated linear f(R, T) gravity model with a single parameter, we studied the strong energy condition (SEC), the weak energy condition (WEC), the null energy condition (NEC), and the dominant energy condition (DEC) under the simplest non‐minimal matter geometry coupling with a perfect fluid distribution. The model parameter is constrained by energy conditions and a single‐parameter proposed equation of state (EoS), resulting in the compatibility of the f(R, T) models with the accelerated expansion of the universe. It is seen that the EoS parameter illustrates the quintessence phase in a dominated accelerated phase, pinpoint to the cosmological constant yields as a prediction the phantom era. Also, the present values of the cosmological constant and the acceleration of the universe are used to check the viability of our linear f(R, T) model of gravity. It is observed that the positive behavior of DEC and WEC indicates the validation of the model. In contrast, SEC is violating the condition resulting in the accelerated expansion of the universe.

Isotropic compact stars in 4D Einstein–Gauss–Bonnet gravity

Recently it has been proposed that the Gauss–Bonnet coupling parameter of Lovelock gravity may suitably be rescaled in order to admit physically viable models of celestial phenomena such that higher curvature effects are active in standard four dimensions as opposed to the usual higher dimensions. We investigate the consequences of this modification in the context of stellar modelling. The evolution of perfect fluid distributions is governed by the pressure isotropy condition and through stipulation of one of the metric potentials complete models emerge from solutions of the master differential equation. New classes of exact solution with this approach have been reported. One particular model is analysed in detail and shown to comport with elementary physical requirements demanded of realistic compact stars suggesting that the modified theory is not inconsistent with observations.

Stability of anisotropic perturbed Einstein universe in f(R,T) theory

The aim of this paper is to investigate the stability of Einstein static cosmos using anisotropic homogeneous perturbations in the background of [Formula: see text] theory in which [Formula: see text] and [Formula: see text] express the Ricci scalar and trace of the stress–energy tensor, respectively. To accomplish this work, we consider perfect fluid distribution and adopt small anisotropic perturbations in the scale factors and matter contents. We develop static and perturbed field equations that are simplified by using equation of state parameter. For the specific models of [Formula: see text] theory with conserved and non-conserved stress–energy tensor, the Einstein solutions are explored and their stability regions are analyzed graphically. We conclude that the static Einstein stable universe with anisotropic perturbations exists in this framework contrary to general relativity.

Exact solutions of Einstein field equations in perfect fluid distribution using Lie symmetry method

The exact non-static accelerating solutions of Einstein field equations in perfect fluid distribution with nonzero shear in the texture gas dominated universe corresponding to an indefinite non-degenerate metric in cartesian coordinates are obtained in a gravitational field of Petrov type D. Lie symmetry method is used for reduction and finding trigonometric solutions. By following multiplier approach, the conservation laws are obtained. The graphical representations are also shown.