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This paper investigated the anisotropic quintessence stars in the f (R , ϕ) theory of gravity, where R is the Ricci scalar and ϕ is the scalar potential. We investigated the field equations of the f (R , ϕ) theory of gravity by using the Krori–Barua technique. We have determined that all the obtained solutions are free from central singularity and potentially stable. The observed values of mass and radius of the different strange stars Her X1, SAXJ1808.4-3658, and 4U1820-30 have been used to calculate the values of unknown constants in the Krori and Barua metric. The physical phenomena of stars, such as energy density, pressure components, anisotropy, sound speeds, equation of state parameters, energy conditions and redshift have been investigated in detail. [ABSTRACT FROM AUTHOR]

This paper aims to conduct an extensive examination of hyperbolically symmetrical static fluid distributions, wherein a precise analysis of their physical characteristics is carried out in the background of modified f (G , T) gravity, where G and T stands for Gauss Bonnet invariant and energy-momentum trace, respectively. The outcomes reveal that the energy density exhibits negative value, thus implying that any utilization of such fluids necessitates extremely demanding circumstances where quantum effects would be significantly influential. Furthermore, it has been determined that these fluid distributions cannot take the vicinity surrounding their central point of symmetry and leave behind an empty vacuum cavity in its place. Additionally, an appropriate definition for mass function and the complexity factor is determined. Eventually, we exhibit a broad strategy for accomplishing particular solutions and showcase several instances of exact analytical solutions in the presence of f (G , T) correction terms. [ABSTRACT FROM AUTHOR]

We investigate the behavior of expansion free collapsing fluids, as studied by L. Herrera, A. Di Prisco and J. Ospino [Symmetry 15 (2023) 754], in the framework of f (R) gravity, which represents a modification of Einstein's general relativity by establishing a function of the Ricci scalar R in the gravitational action. We explore dynamical equations from Bianchi identities that demonstrate the motion and evolution of physical systems under the influence of gravitational fields. We match the inner and outer geometries of spacetime on the hypersurface to develop junction conditions by using the Misner–Sharp formalism. This allows us to identify the connection between mass functions for the inner and outer space as well as the relationship for heat flux q and radial pressure ℙ r . We also investigate analytical solutions of dissipative fluid distribution that fulfill the vanishing expansion condition together with the vanishing complexity factor constraint. For this, we introduce new constraints that permit the integration of the complex system in f (R) gravity. Next, we extract a set of differential equations that explain the dynamical structure of the dissipative spheres both in geodesic and non-geodesic fluids. Furthermore, we explore the physical characteristics of the obtained solutions, such as heat flux, energy density, shear stress, fluid's temperature along with tangential and radial pressure, to assess their viability in describing real astrophysical systems. [ABSTRACT FROM AUTHOR]

Here, we analyse the distribution of self-gravitating collapsing fluid to identify the factors accountable for the energy–density inhomogeneity with the systematic construction in modified Gauss–Bonnet (GB) gravity, by taking the space–time which is spherically symmetric. The modified Einstein's equations help us to observe the variation in the mass function due to different quantities. The dynamical equations and two differential equations for Weyl curvature are formulated, and used to explore the quantities responsible for the inhomogeneity. Irregularity in the fluid is analysed by taking various cases of fluid, under the effects of f (G) theory, where G is a Gauss–Bonnet term. [ABSTRACT FROM AUTHOR]

This work discusses the responsible quantities of the emergence inhomogeneity by taking locally anisotropic radiating fluid in f (G , T) theory, where T and G indicate the trace of stress energy tensor and Gauss–Bonnet terms. The temporal and radial change in mass function is observed with the help of a modified version of Einstein's field equations. To observe the dynamics of self-gravitating fluid, the dynamical equations and differential equations for conformal tensor are constructed, which help to understand the role of correction terms, Weyl curvature, and fluid parameter in the energy–density irregularity. Various forms of fluid are addressed to meet the desired results. [ABSTRACT FROM AUTHOR]

Employing the Palatini version of f (R) gravity theory (R being the Ricci scalar), this paper describes the evolution of a radiating axially symmetric fluid and its changeover to a non-radiating state. Orthonormal tetrad formalism is taken into account because this technique is easier to use and yields simple tensors leaving the predictions of the theory unchanged. Effective tetrad components of the heat flux, the vorticity vector and the shear tensor are evaluated along with the two parts (electric and magnetic) of Weyl curvature tensor. Furthermore, certain structure scalars are procured from the orthogonal division of the Riemann tensor to figure out basic characteristics of the fluid source like the energy density, stress anisotropy and the heat flux. Few differential equations are worked out to gain insight into the consistency of modified field equations while the system transits from its radiating to equilibrium state. [ABSTRACT FROM AUTHOR]

Despite coming across quite effective definitions of complexity in terms of many modified theories of gravity, it still has a question about its existence in f(T) gravity, where the torsion scalar T is accountable for gravitational impacts. The emergence of complexity factor is due to division of intrinsic curvature in an orthogonal way as described by Herrera (Phys Rev D 97:044010, 2018). To initiate the analysis, we reckon the interior region is like a spherically symmetric static configuration filled by the locally anisotropic fluid and exteriorly associated with a spherical hypersurface. In this framework, we acquire the f(T) field equations and utilize the already formulated relationship between the intrinsic curvature and the conformal tensor to perform our analysis. We bring into action the definitions of the two frequently availed masses (Tolman and Misner–Sharp) for spherical composition and investigate the appealing correlation between them and the conformal tensor. The impact of the local anisotropy and the homogeneity and inhomogeneity of energy density has substantial importance in this regard. We build up some relation in terms of already defined variables and interpret the complexity as a single scalar Y TF . It deduce that this factor vanished when the fluid content is homogenous and also when the impact of two anisotropic terms cancel out in the case of inhomogeneous fluid content. We determine a few definite interior solutions which fulfill the criterion of vanishing scalar Y TF . Certain defined ideas in fulfillment of the vanishing complexity factor constraint, are applied for f(T) gravity. [ABSTRACT FROM AUTHOR]

One of the possible potential candidates for describing the universe's rapid expansion is modified gravity. In the framework of the modified theory of gravity f(R, G), this work features the materialization of anisotropic matter such as compact stars. Specifically, to learn more about the physical behavior of compact stars, the radial, and tangential pressures as well as the energy density of six stars namely H e r X − 1 , SAXJ1808.4-3658, 4U1820-30, PSR J 1614 2230, VELA X-1, and Cen X-3 are calculated. Herein, the modified theory of gravity f(R, G) is disintegrated into two parts i.e. the tanh hyperbolic f(R) model and the three different f(G) models. The study focuses on graphical analysis of compact stars wherein the stability aspects, energy conditions, and anisotropic measurements are mainly addressed. Our calculation revealed that for the positive value of parameter n of the model f(G), all the six stars behave normally. [ABSTRACT FROM AUTHOR]

This manuscript is devoted to analyze hyperbolically symmetric non-static fluid distribution incorporated with heat flux and electromagnetic field. We have developed a general framework in order to examine the dynamic regime of the matter configuration which eventually results in the static spacetime. With the aim of doing this, we constructed the Einstein-Maxwell (EM) field equations and obtained the conservation equation. Furthermore, the formulation of mass function indicates the presence of the negative energy density, which leads towards the significant quantum implications. Taking into account the transport equation, we have observed the thermodynamical attributes of the fluid. Additionally, quasi- homologous constraint has been utilized to construct several models. We have deduced the worthwhile applications of the astrophysical objects by evaluating several analytical solutions in terms of the kinematical variables. [ABSTRACT FROM AUTHOR]

A thorough examination of static hyperbolically symmetric matter configuration in the context of Palatini f(R) gravitational theory has been carried out in this manuscript. Following the work of Herrera et al. (Phys. Rev. D 103: 024037, 2021) we worked out the modified gravitational equations and matching conditions using the Palatini technique of variation in Einstein–Hilbert action. It is found from the evaluations that the energy density along with the contribution of dark source terms is inevitably negative which is quite useful in explaining several quantum field effects, because negative energies are closely linked with the quantum field theory. Such negative energies may also assist in time-travel to the past and formation of artificial wormholes. Furthermore, we evaluated the algebraic expressions for the mass of interior hyperbolical geometry and total energy budget, i.e., the Tolman mass of the considered source. Also, the structure scalars are evaluated to analyze the properties of matter configuration. Few analytical techniques are also presented by considering several cases to exhibit the exact analytical static solutions of the modified gravitational equations. [ABSTRACT FROM AUTHOR]

This work probes the influence of charge field on the unique stellar structure, regarded as gravastar, under the corrections of f () theory, i.e. (ℬ) theory, where is named as Gauss–Bonnet invariant. The gravastar has also been recognized as an alternate candidate of black hole structure and is illustrated by three distinct regions termed as (1) the exterior (2) the intermediate thin shell (3) the interior domain. We discussed the mathematical solutions for each of three regions separately with the assistance of different equation-of-states (EoS). The exterior charged vacuum domain is expressed by the Reissner–Nordström solution. The central region is illustrated by the EoS, i.e. a positive pressure of ultra-relativistic matter is equal to the energy density. Whereas, the interior domain reflects that the negative pressure is equal to energy density and manifests a non-attractive force over the central spherical shell. We deduce that in the context of ℬ theory, the nonsingular charged model with distinct physical features, such as energy, length, entropy, is physically viable and consistent. [ABSTRACT FROM AUTHOR]

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. f (G) gravity), where G 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 f (G) degrees of freedom. Moreover, the impact of the dark source terms of f (G) gravity on the system is analyzed which revealed that the complexity of the fluid configuration is increased due to the modified terms. [ABSTRACT FROM AUTHOR]

This paper copes with the issue of analyzing the conditions to check the stability of the pressure isotropy condition by taking into account a spherically symmetric dissipative astrophysical configuration with the Palatini f (R) gravity theory. We work out a differential equation in terms of the Weyl scalar that has a crucial part in the analysis of evolution of considered system. Using this equation, we devise another stellar equation that characterizes the evolution of anisotropic factor. Later, we assume an axially symmetric configuration and extend our analysis for that particular symmetry. It is worth-observing that the physical factors responsible for compelling an initially isotropic object to trigger pressure anisotropy incorporate energy density, dissipative flux and shear in fluid flow. [ABSTRACT FROM AUTHOR]

The aim of this paper is to generalize the definition of complexity for the static self-gravitating structure in f  (R, T, Q) gravitational theory, where R is the Ricci scalar, T is the trace part of energy–momentum tensor, and Q ≡ R αβ T  αβ. In this context, we have considered locally anisotropic spherical matter distribution and calculated field equations and conservation laws. After the orthogonal splitting of the Riemann curvature tensor, we found the corresponding complexity factor with the help of structure scalars. It is seen that the system may have zero complexity factor if the effects of energy density inhomogeneity and pressure anisotropy cancel the effects of each other. All of our results reduce to general relativity on assuming f  (R, T, Q) = R condition. [ABSTRACT FROM AUTHOR]

In this article, we explore a few less complex models for the charged spherically symmetric structures. We take an anisotropic and static fluid distribution experiencing co-moving coordinate system. After using orthogonal splitting technique, we formulate two different formulations of stellar mass that would be then expressed in the values of structure scalars. A structure scalar Y T F is found to complexity factor that would lead us to study various characteristics of the relativistic spherical interiors. It is noticed that this factor disappears for both homogeneous isotropic fluids and inhomogeneous anisotropic gravitating source. Finally, we evaluate some theoretical models after using vanishing complexity condition. • We explore less complex models for the charged spheres. • We formulate two different forms of stellar mass in the structure scalars. • We evaluate some theoretical models with vanishing complexity condition. [ABSTRACT FROM AUTHOR]

The aim of this paper is to explore some physically viable aspects for the possible emergence of compact stars in theory of gravity with some particular models, where and are Gauss-Bonnet invariant and trace of stress-energy tensor, respectively. We present basic formalism of this modified theory in the presence of anisotropic source. We explore some realistic aspects using the energy conditions with physical parameters. Three distinct known star models namely, and , are used for this systematic investigation. The physical behavior of anisotropic stresses, energy density, energy conditions, measure of anisotropy and stability of compact stars are discussed through plots. We conclude that compactness at the core of a star model increases and energy conditions hold. [ABSTRACT FROM AUTHOR]

We study the influence of Palatini $f(R)$ gravity and tilted observer on the dynamics of Lemaître-Tolman-Bondi space-time in the presence of electromagnetic field. The imperfect charged fluid seen by tilted observer is considered in comparison with charged dust fluid seen by nontilted observer. We develop the relations between tilted and nontilted variables by including electric charge in Palatini $f(R)$ gravity. In this framework, we explore the evolution of energy density inhomogeneities for tilted and nontilted observers by calculating the energy conservation laws for charged fluid. Finally, we evaluate a constraint on the electric charge in the collapse of stellar objects, which leads to the instability of nontilted congruence. [ABSTRACT FROM AUTHOR]

This manuscript studies the inhomogeneity in the energy density for the relativistic dynamical charged system by invoking the outcomes coming from the considered anisotropic distribution of radiating fluid. We use newly developed f (G , T 2) theory, which was proposed by the addition of T 2 = T ζ ξ T ζ ξ in the usual action of f (G ,) gravity. We construct relativistic field equations for a specific model f (G , T 2) = λ T 2 + G (1 + G α) , to examine the gravitational structure in the influence of electromagnetic filed. We use dynamical expressions and differential equations for Weyl tensor for the inspection of sources of irregularities. By exploring special cases in the non-radiating and radiating scenarios, the irregularity elements for a fluid are examined. These special cases show that modified terms and charge have a considerable impact on the fluid inhomogeneity. • This manuscript studies the inhomogeneity in the energy density for the relativistic charged spherical system. • After constructing the evolution equations for Weyl tensor, we analyzed the sources of irregular energy density over the initially homogeneous objects. • The structure variable is found to be responsible for pushing the locally anisotropic system to enter in the inhomogeneous phase. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study role of adiabatic index (stiffness parameter) on the evolution of an anisotropic collapsing spherical self-gravitating system in Palatini f( R) gravity. In this scenario, we construct dynamical equation with the help of contracted Bianchi identities of the effective dark sources as well as usual matter. The perturbation approach is applied on the physical variables which consequently perturbes the Ricci scalar. We discuss instabilities both for zero and non-zero expansion. It is shown that instability range of the given system depends upon energy density profile, anisotropic pressure and chosen f( R) model in both scenarios. However, the adiabatic index is not helpful in expansion-free instability analysis at N and pN regimes. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the role of electromagnetic field and generalized Carrol-Duvvuri-Trodden-Turner (CDTT) model on the existence of homogeneous energy density. For this purpose, we model spherical star with anisotropic matter distribution dissipating in the mode of heat and radiation density. To develop a relationship between the Weyl tensor and matter parameters, we construct two evolution equations. We explore inhomogeneity parameters for particular cases of non-dissipative and dissipative matter distributions. It is concluded that in addition to other fluid variables higher order f( R) corrections, relaxation processes and electromagnetic field affect the energy density inhomogeneity of spherical stars. [ABSTRACT FROM AUTHOR]

We explore the factors of inhomogeneity in the spherically symmetric distribution of collapsing fluid under the effect of electromagnetic field in f (G) theory. Modified Bianchi identities and two significant equations for the Weyl tensor are formulated to get help in the analysis. Causes of inhomogeneity are analyzed by considering the non-radiating and radiating charged fluid. The non-dissipative type of fluid contains pressureless, isotropic and anisotropic fluid. It is observed that for anisotropic fluid, the inhomogeneity corresponds to the structure scalar. For dissipative dust, the effects of relaxation time in terms of electromagnetic field are brought out. • We explore the factors of inhomogeneity in the spherically symmetric matter distribution under Maxwell-f(G) theory. • Modified Bianchi identities and evolution equations for the Weyl tensor are formulated for the required results. • Causes of inhomogeneity are analyzed by considering the non-radiating and radiating charged fluid. [ABSTRACT FROM AUTHOR]

In this paper, we study the effects of polynomial f( R) model on the stability of homogeneous energy density in self-gravitating spherical stellar object. For this purpose, we construct couple of evolution equations which relate the Weyl tensor with matter parameters. We explore different factors responsible for density inhomogeneities with non-dissipative dust, isotropic as well as anisotropic fluids and dissipative dust cloud. We find that shear, pressure, dissipative parameters and f( R) terms affect the existence of inhomogeneous energy density. [ABSTRACT FROM AUTHOR]

The objective of this paper is to study the stability of an adiabatic anisotropic collapsing sphere in the context of Palatini f( R) gravity. In this framework, we construct the collapse equation with the help of the contracted Bianchi identities of the effective as well as the usual energy-momentum tensor. The perturbation scheme is applied on the fluid variables which accordingly cause a perturbation on the Ricci scalar. We explore the instability ranges in the Newtonian and post-Newtonian regimes. It is concluded that the stability of the star is governed by adiabatic index Γ1, which depends on the energy density profile, anisotropic pressure and dark source terms of the chosen f( R) model. We also explore our results when f( R)→ R. [ABSTRACT FROM AUTHOR]

This study focuses on the impact of the cosmological constant on hyperbolically symmetric matter configurations in a static background. I extend the work of Herrera et al. 2021. and describe the influences of such a repulsive character on a few realistic features of hyperbolical anisotropic fluids. After describing the Einstein- Λ equations of motion, I elaborate the corresponding mass function along with its conservation laws. In our study, besides observing negative energy density, I notice the formation of a Minkowskian core as matter content is compelled not to follow inward motion near the axis of symmetry. Three families of solutions are found in the Λ -dominated epoch. The first is calculated by keeping the Weyl scalar to a zero value, while the second solution maintains zero complexity in the subsequent changes of the hyperbolical compact object. However, the last model encompasses stiff fluid within the self-gravitating system. Such a type of theoretical setup suggests its direct link to study a few particular quantum scenarios where negative behavior of energy density is noticed at the Λ -dominated regime. [ABSTRACT FROM AUTHOR]

This paper is devoted to understanding a few characteristics of static irrotational matter content that assumes hyperbolical symmetry. For this purpose, we use metric f (R) gravity to carry out our analysis. It is noticed that the matter distribution cannot fill the region close to the center of symmetry, thereby implying the existence of an empty core. Moreover, the evaluation of the effective energy density reveals that it is inevitably negative, which could have utmost relevance in understanding various quantum field events. To derive the structure scalars, we perform the orthogonal splitting of the Riemann tensor in this modified gravity. Few relationships among matter variables and both Tolman and Misner Sharp are determined. Through two generating functions, some hyperbolically symmetric cosmological models, as well as their physical interpretations, are studied. To delve deeply into the role of f (R) terms, the model of the less-complex relativistic system of Einstein gravity is presented. [ABSTRACT FROM AUTHOR]

The present paper is devoted to investigate the possible emergence of relativistic compact stellar objects through modified f(R, T) gravity. For anisotropic matter distribution, we used Krori and Barura solutions and two notable and viable f(R, T) gravity formulations. By choosing particular observational data, we determine the values of constant in solutions for three relativistic compact star candidates. We have presented some physical behavior of these relativistic compact stellar objects and some aspects like energy density, radial as well as transverse pressure, their evolution, stability, Eos parameters, measure of anisotropy and energy conditions. [ABSTRACT FROM AUTHOR]