Inhomogeneous Energy Density Research Articles

Causes of Energy Density Inhomogeneity in Energy Momentum Squared Gravity

Causes of Energy Density Inhomogeneity in Energy Momentum Squared Gravity

Shear-free inhomogeneous energy density in 4D Einstein-Gauss-Bonnet spherical systems

We explore the inhomogeneity factors for the initially regular relativistic spheres in 4D-Einstein-Gauss-Bonnet (EGB) theory. The corresponding equations of motion are derived once the generic expressions for the kinematical variables are obtained for spherically symmetric self-gravitating system. By using the non-zero divergence of the stress-energy tensor, the independent components of Bianchi identities are constructed. To enable a thorough explanation of the inhomogeneity of the particular shear free matter distribution, we computed two distinct components of evolution equations employing the Weyl tensor. We then investigate the requisite variables for the irregularity by looking at particular scenarios in both the adiabatic and non-adiabatic domains. These instances demonstrate how, in addition to other factors, the Gauss-Bonnet terms contribute to the regularity requirements of the collapsing fluid.

Anisotropic stellar evolution and exotic matter

In this paper, we discuss the stability of isotropic pressure conditions for a spherically symmetric dissipative fluid distribution in the framework of f(G,T) gravity. We consider the fluid to be composed of seen and exotic matter particles. The Gauss Bonnet terms represent exotic matter particles. For the physical significance of the pressure isotropy conditions, we transform the system into the hydrostatic equilibrium approximation. We observe the presence of shear, dissipative fluxes, energy density inhomogeneities, and prominently, the exotic matter tends to abandon isotropy leading to pressure anisotropy. It is found that exotic matter and dissipation are major factors that induce matter anisotropy in the evolving stellar system. In order to discuss the physical significance of the stellar model in f(G,T) gravity, the behaviour of stellar structure is explored according to the observational data of a compact star 4U1820 − 30. It is found that f(G,T) terms indicating the exotic material in the stellar model plays a vital role in governing the dynamics of the evolution. To strengthen the results, we also incorporate some arguments by choosing an axially symmetric case.

Energy density inhomogeneities with self-gravitating charged fluid in modified teleparallel gravity

In this paper, we analyze energy density inhomogeneities for charged fluid configuration in the background of [Formula: see text] theory and recognize its prime features as computed in GR. The dynamical equations are composed employing Bianchi identities for the standard, [Formula: see text] extra terms, and energy-momentum tensor for the electromagnetic field. We evaluate various mathematical models of dissipative and anisotropic fluid distributions in-plane symmetry under [Formula: see text] gravity. To proceed with the investigation, we design the [Formula: see text] field equations, kinematical quantities, and mass function. We analyzed dynamical variables and Ellis equations in terms of our considered theory. To examine the associated inhomogeneity factors, specific scenarios are illustrated alongside and without dissipation. Within a non-radiating situation, we analyze dust and isotropic and anisotropic matter in the state of electric charge. We examine the inhomogeneity factor of a dissipative fluid via a charged dust haze. We derive that the electromagnetic field fosters matter inhomogeneity, but additional curvature factors make the entire structure more homogenous as time passes.

Analytical Modelling of Inhomogeneous Energy Density Driven (IEDD) Instability in a Magnetized Dusty Plasma Cylinder

Analytical Modelling of Inhomogeneous Energy Density Driven (IEDD) Instability in a Magnetized Dusty Plasma Cylinder

Impact of charge on the complexity of static cylindrical system

This work examines the complexity of charged static cylindrical object with anisotropic matter configuration in the background of energy–momentum squared gravity. For this purpose, we construct the field equations, the non-conservation equation and investigate the celestial structure. We evaluate the mass functions through both C-energy as well as Tolman mass formulae. Numerous factors, such as anisotropic pressure, inhomogeneous energy density and charge, etc have an impact on the complexity of the structure under consideration. The orthogonal splitting of the Riemann tensor yields two structure scalars. Among these both, the factor incorporating all the physical parameters of the self-gravitating system is named as the complexity factor. The complexity-free constraint is employed to compute charged static solutions for the Gokhroo–Mehra model as well as the polytropic equation of state. We conclude that the inclusion of charge reduces the complexity of anisotropic system.

Electromagnetic effects on the complexity of static cylindrical object in f(G, T) gravity

In this paper, we investigate complexity of anisotropic cylindrical object under the influence of electromagnetic field in f(G, T) theory, where G and T indicate the Gauss–Bonnet term and trace of the stress–energy tensor, respectively. For this purpose, we calculate the modified field equations, non-conservation equation and mass distributions that assist in comprehending the structure of astrophysical objects. The Riemann tensor is divided into different structure scalars, among which one is called the complexity factor. This factor is used to measure complexity of the system due to the involvement of inhomogeneous energy density, anisotropic pressure and charge. The vanishing of the complexity factor is employed as a constraint to formulate charged static solutions for the Gokhroo–Mehra model and polytropic equation of state. We conclude that the presence of charge reduces the complexity of the anisotropic system.

Complexity factor for static cylindrical system in energy-momentum squared gravity

This paper investigates some physical features that give rise to complexity within the self-gravitating static cylindrical structure coupled with anisotropic distribution in the energy-momentum squared gravity. To accomplish this, we formulate the modified field equations and explore the structure of the astronomical body. The C-energy and Tolman mass are also calculated to discuss the matter distribution. We then obtain some structure scalars via orthogonal splitting of the Riemann tensor. Since, the complexity of the considered structure is influenced by a variety of variables, including anisotropic pressure and inhomogeneous energy density, etc. thus, we adopt the factor $\mathcal{Y}_{TF}$ as the complexity factor. Further, the complexity-free condition along with the Gokhroo-Mehra model and polytropic equation of state are taken to generate their corresponding solutions. We deduce that the inclusion of additional terms of this modified theory leads to a more complicated system.

Implications for vanishing complexity in dynamical spherically symmetric dissipative self-gravitating fluids

The complexity factor, originally based on a probabilistic description of a physical system, was re-defined by Herrera et al. for relativistic systems. This involves an assessment of the energy density inhomogeneity, anisotropic and shear stresses, and in the case of radiating collapse, the effects of heat flux. Already well integrated into the modelling of static configurations, the complexity factor is now being studied with respect to dynamical, self-gravitating systems. For static systems, the constraint of vanishing complexity is typically used however for the non-static case, the physical viability of the vanishing condition is less clear. To this end, we consider the ideal case of vanishing complexity in order to solve for the time-dependent gravitational potentials and generate models. We find that vanishing complexity constrains the metric to be of a form similar to that of Maiti’s conformally flat metric.

Complexity analysis of charged dynamical dissipative cylindrical structure in modified gravity

This article focuses on the formulation of some scalar factors which are uniquely expressed in terms of matter variables for dynamical charged dissipative cylindrical geometry in a standard gravity model \(\mathcal {R}+\Phi \mathcal {Q}\) (\(\Phi \) is the coupling parameter, \(\mathcal {Q}=\mathcal {R}_{\varphi \vartheta }\mathcal {T}^{\varphi \vartheta }\)) and calculates four scalars by orthogonally decomposing the Riemann tensor. We find that only \(\mathcal {Y}_{TF}\) involves inhomogeneous energy density, heat flux, charge and pressure anisotropy coupled with modified corrections, and thus call it as complexity factor for the considered distribution. Two evolutionary modes are discussed to study the dynamics of cylinder. We then take the homologous condition with \(\mathcal {Y}_{TF}=0\) to calculate unknown metric potentials in the absence as well as presence of heat dissipation. The stability criterion of the later condition is also checked throughout the evolution by applying some constraints. We conclude that the effects of charge and modified theory yield more complex system.

Complexity of a dynamical dissipative cylindrical system in non-minimally coupled theory

This paper aims to formulate certain scalar factors associated with the matter variables for a self-gravitating non-static cylindrical geometry by considering a standard model R+ζQ of f(R,T,Q) gravity, where Q=RφϑTφϑ and ζ is the arbitrary coupling parameter. We split the Riemann tensor orthogonally to calculate four scalars and deduce YTF as a complexity factor for the fluid configuration. This scalar incorporates the influence of the inhomogeneous energy density, heat flux and pressure anisotropy along with correction terms for the modified gravity. We discuss the dynamics of the cylinder by considering the two simplest modes of structural evolution. We then take YTF=0 with a homologous condition to determine the solution for the dissipative as well as non-dissipative scenarios. Finally, we discuss the criterion under which the complexity-free condition shows stable behavior throughout the evolution. It is concluded that the complex functional of this theory results in a more complex structure.

Complexity of dynamical cylindrical system in f(G, T) gravity

The purpose of this paper is to formulate a complexity factor for a non-static cylindrical structure in the background of [Formula: see text] gravity, where [Formula: see text] and [Formula: see text] represent the Gauss–Bonnet term and trace of the energy–momentum tensor, respectively. Different physical factors such as inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms are considered as candidates of complexity. In order to determine a complexity factor encompassing the essential aspects of the system, we apply the technique of orthogonal splitting to the Riemann tensor. We also study evolution of the cylinder through two modes: homologous and homogeneous. Further, we utilize the complexity-free and homologous conditions to examine the dissipative and non-dissipative self-gravitating system. Finally, the factors responsible for inducing complexity during the evolution system are inspected. We deduce that the modified terms in [Formula: see text] gravity make the system more complex.

Complexity of static sphere in energy–momentum squared gravity

In this paper, we study complexity of a static spherically symmetric object containing anisotropic fluid in the background of energy–momentum squared gravity (EMSG). We formulate the field equations and describe the energy content of the fluid via Misner–Sharp as well as Tolman mass definitions. In order to compute the complexity factor, the Riemann tensor is orthogonally split to produce structure scalars which incorporate the fundamental properties of the system. The scalar involving anisotropic pressure and inhomogeneous energy density is chosen as the complexity factor. We consider a minimally coupled model to formulate the condition for vanishing complexity which is employed to formulate two solutions. It is concluded that additional matter source terms appearing due to energy–momentum squared gravity increase the complexity of the system.

Complexity for dynamical anisotropic sphere in [formula omitted] gravity

This paper is devoted to the formulation of a complexity factor for dynamical anisotropic sphere in the framework of f(G,T) gravity, where G is the Gauss–Bonnet invariant and T is the trace of energy–momentum tensor. Inhomogeneous energy density, anisotropic pressure, heat dissipation and modified terms create complexity within the self-gravitating system. We evaluate the structure scalars by orthogonal splitting of the Riemann tensor to evaluate a complexity factor which incorporates all the fundamental properties of the system. Moreover, we examine the dynamics of the sphere by assuming homologous mode as the simplest pattern of evolution. We also discuss dissipative as well as non-dissipative scenarios corresponding to homologous and complexity free conditions. Finally, we establish a criterion under which the complexity free condition remains stable throughout the process of evolution. We conclude that the presence of dark source terms of f(G,T) gravity increase the system’s complexity.

Role of energy–momentum squared gravity on the dynamics of charged dissipative plane symmetric collapse

This paper deals with the dynamics of charged plane symmetric collapse with dissipative fluid distribution in the framework of energy–momentum squared gravity. For this purpose, we consider non-static plane symmetric spacetime in the inner and static charged Vaidya spacetime in the outer regions of a star. We use Darmois junction conditions to match the interior and exterior geometries and find that masses of both spacetimes are identical if and only if their correspondence charges are same. To investigate the dynamics of the system, we apply Misner–Sharp and Müler–Israel–Stewart approaches to formulate dynamical as well as transport equations, respectively. We then couple these equations to analyze the effect of physical quantities and modified terms on the collapse rate. A relation among Weyl tensor, electromagnetic field and fluid variables, is also developed. Due to the influence of charge, anisotropic pressure and modified terms, the spacetime is not conformally flat. Further, we assume isotropic fluid and ignore the impact of electromagnetic field which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the presence of a charge, effective pressure, heat flux and additional terms of this gravity.

Complexity factor for anisotropic self-gravitating sphere in Rastall gravity

This paper investigates the new definition of complexity factor for the case of irrotational spherical relativistic structure in the Rastall theory of gravity (RTG). To do so, we assumed static spherically symmetric metric with anisotropic self-gravitating fluid. We studied Rastall field equations, generalized nonconservation equation, mass function and physical impacts of Rastall parameter [Formula: see text] on various material variables by employing certain observational data of compact objects like PSR J1614-2230, 4U1608-52, SAX J 1808.4-3658, 4U1820-30 and Vela X-1. We obtained structure scalars through orthogonal decomposition of the curvature tensor and then utilize these scalars to find the complexity factor of the self-gravitating spherical structure. We examined that the vanishing complexity factor condition is an effective energy density inhomogeneity and an effective anisotropy of pressure which must cancel each other, employed the condition [Formula: see text]. Moreover, we also depicted the solutions of interior formation of spherical stellar object regarding to this vanishing complexity condition. Finally, it is found that the complexity of the system enhances due to the presence of nonminimal to curvature matter couple parameter [Formula: see text]. It is very fascinating to report here that these outcomes could be recovered back to former solutions about complexity factor in General Relativity (GR) by imposing [Formula: see text].

Study of stellar structures in f(ℛ,𝒯μν𝒯μν) theory

This paper deals with the dynamics of cylindrical collapse with anisotropic fluid distribution in the framework of [Formula: see text] gravity. For this purpose, we consider non-static and static cylindrical spacetimes in the inner and outer regions of a star, respectively. To match both geometries at the hypersurface, we consider the Darmois junction conditions. We use the Misner–Sharp technique to examine the impacts of correction terms and effective fluid parameters on the dynamics of a cylindrical star. A correlation between the Weyl tensor and physical quantities is also developed. The conformally flat condition is not obtained due to the influence of anisotropic pressure and higher-order nonlinear terms. Further, we assume isotropic fluid and specific model of this theory which yields the conformally flat spacetime and inhomogeneous energy density. We conclude that the collapse rate reduces as compared to general relativity due to the inclusion of effective pressure and additional terms of this theory.

Influence of f(G) gravity on the complexity of relativistic self-gravitating fluids

In this paper, we extend the notion of complexity for the case of nonstatic self-gravitating spherically symmetric structures within the background of modified Gauss–Bonnet gravity (i.e. [Formula: see text] gravity), where [Formula: see text] denotes the Gauss–Bonnet scalar term. In this regard, we have formulated the equations of gravity as well as the relations for the mass function for anisotropic matter configuration. The Riemann curvature tensor is broken down orthogonally through Bel’s procedure to compose some modified scalar functions and formulate the complexity factor with the help of one of the scalar functions. The CF (i.e. complexity factor) comprehends specific physical variables of the fluid configuration including energy density inhomogeneity and anisotropic pressure along with [Formula: see text] degrees of freedom. Moreover, the impact of the dark source terms of [Formula: see text] gravity on the system is analyzed which revealed that the complexity of the fluid configuration is increased due to the modified terms.

Structure scalars and their evolution for massive objects in f(R) gravity

In this manuscript, the Riemann tensor is split orthogonally to get five scalar functions known as structure scalars which have significance to gain insight into the composition and structure of spherically symmetric self-gravitating objects. Certain stellar equations are then evaluated to gather information about physical characteristics of such astrophysical objects. These stellar equations are further written in terms of acquired structure scalars so that the basic properties such as pressure anisotropy and energy density inhomogeneity of the fluid under consideration can be explored. Also, we have explored few static spherically symmetric solutions to show significance of structure scalars in the background of f(R) gravity.

Complexity of dynamical sphere in self-interacting Brans\u2013Dicke gravity

This paper aims to derive a definition of complexity for a dynamic spherical system in the background of self-interacting Brans–Dicke gravity. We measure complexity of the structure in terms of inhomogeneous energy density, anisotropic pressure and massive scalar field. For this purpose, we formulate structure scalars by orthogonally splitting the Riemann tensor. We show that self-gravitating models collapsing homologously follow the simplest mode of evolution. Furthermore, we demonstrate the effect of scalar field on the complexity and evolution of non-dissipative as well as dissipative systems. The criteria under which the system deviates from the initial state of zero complexity is also discussed. It is concluded that complexity of the sphere increases in self-interacting Brans–Dicke gravity because the homologous model is not shear-free.