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In this paper, our purpose is to investigate the anisotropic stellar structure caused by f (R , ϕ) modified gravity, where R represents the Ricci scalar and ϕ represents the scalar potential. This study emphasizes the impact of static spherically symmetric stellar structures using anisotropic distribution. Furthermore, an anisotropic matter source is employed to explore the stability of star formations. To get the value of unknown parameters of the compact structures, we compare the Schwarzschild metric to external geometry. Moreover, we examine the physical attributes of compact objects by presuming a viable f (R , ϕ) = ϕ (R + α R 2) gravity model. We analyze the graphical behavior of density and pressure, the Tolman–Oppenheimer–Volkov equation, energy conditions, mass function, surface redshift, and adiabatic index. It is recognized that all the obtained results deliver emphatic evidence for the stability of our considered realistic stars. [ABSTRACT FROM AUTHOR]

This study deals with the physical aspects of the gravitationally decoupled solutions under f(ℛ) gravity scenario. In doing so, charged anisotropic matter composition is assumed as the parent (seed) source for the static spherically symmetric configuration. Commencing with the Kuchowicz ansatz for the charged static parent matter formation, we establish the Karmarkar condition to thoroughly address the deformed functions and the gravitational aspects of the compact spheres. Besides these, null-complexity and isotropized conditions will enforce to grasp the system’s stability by the inclusion of charge and ℛ+ϖℛ2 factors through graphical trends. [ABSTRACT FROM AUTHOR]

In this paper, we will manifest how polytropic fluids produce effects on an alternate gravitational source, regardless of its features, for spherically symmetric and static spacetimes. For this purpose, we use f(T,풯) modified gravity, which is characterized by the trace of an energy–momentum tensor as 풯 and torsion scalar T, Additionally, using the polytropic equation of state, we will speculate about the distribution of energy among fluids within an astrophysical object. We offer a thorough methodology for identifying generic relativistic polytropes accompanied by the minimal geometric decoupling technique. Ultimately, a few tangible attributes of polytropes along with perfect fluids are observed using the Tolman IV solution, including total pressure, energy interchange, and thermal characteristics. [ABSTRACT FROM AUTHOR]

In this paper, we review a recently offered notion of quasi-static evolution of the axial self-gravitating structures at large scales and the criterium to characterize the corresponding evolutionary aspects under the influence of strong curvature regimes. In doing so, we examine the axial source's dynamic and quasi-static behavior within the parameters of various modified gravity theories. We address the formalism of these notions and their possible implications in studying the dissipative and anisotropic configuration. We initiate by considering higher-order curvature gravity. The Palatini formalism of f (R) gravity is also taken into consideration to analyze the behavior of the kinematical as well as the dynamical variables of the proposed problem. The set of invariant velocities is defined to comprehend the concept of quasi-static approximation that enhances the stability of the system in contrast to the dynamic mode. It is identified that vorticity and distinct versions of the structure scalars Y I , Y II and Y KL play an important role in revealing the significant effects of a fluid's anisotropy. As another example of evolution, we check the influence of Palatini-based factors on the shearing motion of the object. A comparison-based study of the physical nature of distinct curvature factors on the propagation of the axial source is exhibited. This provides the intriguing platform to grasp the notion of quasi-static evolution together with the distinct curvature factors at current time scenario. The importance of slowly evolving axially symmetric regimes will be addressed through the distinct modified gravitational context. Finally, we share a list of queries that, we believe, deserve to be addressed in the near future. [ABSTRACT FROM AUTHOR]

A coupled formulation of the Gauss–Bonnet invariant term G and the energy–momentum trace T term, which provide a modified f(G, T) gravity, has been analyzed in this study. The functional form for the f(G, T) gravity has been taken as f(G, T) = αT + βGn, where α and β are free parameters. The field equations are produced in general, which then used a dust case to extract a novel Hubble parameter. The stability of the assumed model and explanation for the late-time acceleration have been studied by the energy bound. Furthermore, the dynamical variables are used to analyze the behavior of the equation of state parameter by restricting different parameters with respect to the recent observational data. A quintessence-like evolution has been achieved as a result of this study. [ABSTRACT FROM AUTHOR]

In this paper, we study the construction of black string thin-shell wormhole models with generalized Chaplygin gas under the effect of minimally coupled modified gravity with quadratic correction in the Ricci scalar using the "cut and paste" method. We use junction conditions in geometrical representation for matching between two space-times across the hypersurface Σ , recently computed by Rosa (Phys Rev D 103:104069, 2021). In this scenario, we assumed the matter sector is demonstrated by isotropic perfect fluid distribution. We determine the distinct components of Lanczos equations in the context of a considered quadratic model by employing generalized Chaplygin gas. We investigate static stable solutions utilizing radial perturbation in the perspective of the considered gravity. The positive value of the second-order derivative of potential around the throat radius might be interpreted as the stability criterion. For the widest feasible range of model parameters, the impact of mass and equation of state parameter is also investigated via the constructed equations. We also examine the stable and unstable static black string thin-shell wormhole solutions and illustrate them graphically. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the feasibility and the appearance of charged thin-shell wormholes using generalized Chaplygin gas under the influence of minimally coupled f (R , T) gravitational theory. Here, f is a generic function of the scalar curvature R and the trace of stress-energy tensor T. We explore different components of Lanczos equations in the context of a specific f (R , T) functional form, i.e. f (R , T) = R + 2 λ T , by applying junction conditions on field equations. We study static stable solutions using radial perturbation and the generalized Chaplygin gas equation of state (EoS) with the isotropic environment. We investigate the stable (unstable) static wormhole solutions for various physical parametric values and illustrate them graphically. [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]

Even though extended gravity theories have come up with different healthy measures of complexity for spherical and non‐spherical systems, the study of complexity factors for axially symmetric bodies under the influence of strong matter‐field coupling is still up for debate. The formation of complexity factors for static axially symmetric bodies is induced by the cracking of the Riemann curvature tensor in an orthogonal manner as initiated by Herrera et al. [Phys. Rev. D 99, 044049(2019)]. We provide the continuation of this work in the f(R,T,Q)$f(R,T,Q)$ gravitational theory, where Q=RγϱTγϱ$Q=R_{\gamma \varrho }T^{\gamma \varrho }$ that indicates the powerful matter‐field coupling due to the bilateral influence of the curvature and matter tensors. We proceed our analysis by considering axial geometry confined with anisotropic fluid constituents. In this context, we compute the field equations for the system under discussion. To examine the source's energy content, two dynamical equations that correspond to independent coordinates are constructed. The curvature tensor is split into tensorial quantities to formulate the scalar functions (structure scalars), which involve the physical attributes of the source in the domain of high curvature regimes. Among all, three of the scalars YTFj$Y_{TF_j}$'s (j=1,2,3)$(j=1,2,3)$ are nominated as complexity factors, whose inclusion enhances the inhomogeneity of the propagating system. The vanishing complexity factors criteria are set out for the specific form of the cosmic model that provides the favorable setting to minimize the system's complexity and boost its stability. Furthermore, some analytical insights under various backgrounds of the matter spheroids are presented. Even though extended gravity theories have come up with different healthy measures of complexity for spherical and non‐spherical systems, the study of complexity factors for axially symmetric bodies under the influence of strong matter‐field coupling is still up for debate. The formation of complexity factors for static axially symmetric bodies is induced by the cracking of the Riemann curvature tensor in an orthogonal manner as initiated by Herrera et al. [Phys. Rev. D 99, 044049(2019)]. We provide the continuation of this work in the f (R, T,Q) gravitational theory, where Q = RγρTγρ that indicates the powerful matter‐field coupling due to the bilateral influence of the curvature and matter tensors. We proceed our analysis by considering axial geometry confined with anisotropic fluid constituents. In this context, we compute the field equations for the system under discussion. To examine the source's energy content, two dynamical equations that correspond to independent coordinates are constructed. The curvature tensor is split into tensorial quantities to formulate the scalar functions (structure scalars), which involve the physical attributes of the source in the domain of high curvature regimes. Among all, three of the scalars YTFj 's (j = 1, 2, 3) are nominated as complexity factors, whose inclusion enhances the inhomogeneity of the propagating system. The vanishing complexity factors criteria are set out for the specific form of the cosmic model that provides the favorable setting to minimize the system's complexity and boost its stability. Furthermore, some analytical insights under various backgrounds of the matter spheroids are presented. [ABSTRACT FROM AUTHOR]

This paper investigate the impacts of local density perturbations on the stability of self-gravitating compact objects by utilizing cracking technique within the context of f(R, T) gravity, where R and T represent the Ricci scalar, and the trace of energy–momentum, respectively. To achieve this, we developed the hydrostatic equilibrium equation for spherically symmetric spacetime with anisotropic matter configuration and subsequently applied the Krori–Barua spacetime coefficient. Subsequently, the hydrostatic equilibrium equation of the configuration is perturbed by employing the local density perturbations to the system, while considering a barotropic equation of state. To ascertain the validity of the proposed technique, we applied it to several compact stars, including, Her X-1, SAX J1808.4-3658, 4U 1820-30, PSR J1614-2230, Vela X-1, Cen X-3, and RXJ1856-37 and found that all the considered stars exhibit cracking or overturning. This study conclusively highlights the significance of the cracking technique in providing valuable insights into the stability analysis of self-gravitating compact objects. [ABSTRACT FROM AUTHOR]

In this paper, we highlight the variables preserving stability of a very restricted class of anisotropic axial symmetrical compact geometry in the scenario of f (R , T) gravity, where T stands for energy–momentum tensor's trace and R is invariant Ricci curvature. In the framework of f (R , T) gravity, we set up field equations as well as non-conservation equations. We use a perturbation technique for all variables involved in non-conservation equations, field equations, extra curvature terms of modified gravity as well as for considered gravity model (i.e. f (R , T) = R + ζ R n + χ T) to evaluate the collapse equation. We establish certain significant constraints for the stiffness parameter Γ in Newtonian () and post-Newtonian () approximation to study the dynamical instability of a stellar compact configuration. In order to preserve the stability of an anisotropic self-gravitating axially symmetric configuration, we place certain restrictions on physical quantities. To examine the stable and unstable behavior of considered geometry via graphical approaches, we include schematic diagrams at the and eras. [ABSTRACT FROM AUTHOR]

This investigation aims to explore certain variables which are considered responsible for generating pressure anisotropy in dynamical spherically symmetric stellar systems against the background of the stringy-inspired Gauss–Bonnet modification of general relativity. We explore the hydrostatic equilibrium of self-gravitating systems by taking into account the modified form of Tolman–Oppenheimer–Volkoff for the quadratic- f (G) gravitational model. In this respect, we formulate a differential equation in terms of the Weyl curvature scalar, also described as an evolution equation, which is essential for understanding the evolution of the stellar structure. Finally, we conclude that the existence of some fluid variables such as shear, heat flux and the irregular behavior of energy density in the presence of an extra degree f (G) -terms in the fluid flow that are the elements that cause anisotropy in the initially isotropic stellar structure. The comparison of the presented results with those of the classical model shows that they are physically relevant and compatible. [ABSTRACT FROM AUTHOR]

In this manuscript, we evaluate the validity of the horizon first law in the framework of f(R,G)$f(R, \mathcal {G})$ gravity. We propose that the energy and entropy of a black hole must be consistent with their relating integration values. The feasibility of the newly proposed horizon 1st law as a result of equations of motion in f(R,G)$f(R,\mathcal {G})$ gravity, will have significant importance in our illustration. The derivation of black hole energies and entropies in the framework of specific f(R,G)$f(R, \mathcal {G})$ models will be helpful in future research. We study that how the positivity of energy and entropy can impose additional restrictions on the domain of f(R,G)$f(R, \mathcal {G})$ gravity. Moreover, we shall consider a flat FLRW model corresponding to f(R,G)$f(R,\mathcal {G})$ theory and will derive the related Friedman equations. The Cai‐Kim technique will then be used to evaluate the expression for energy flux passing through the horizon in insignificantly small time. In addition, we use the Clausius relation related to the evident boundary as well as the Cai‐Kim technique and the relating Friedmann equations, to find the expression for horizon entropy. In this manuscript, the authors evaluate the validity of the horizon first law in the framework of f (R, G$\mathcal{G}$) gravity. They propose that the energy and entropy of a black hole must be consistent with their relating integration values. The feasibility of the newly proposed horizon 1st law as a result of equations of motion in f (R, G$\mathcal{G}$) gravity, will have significant importance in our illustration. The derivation of black hole energies and entropies in the framework of specific f (R, G$\mathcal{G}$) models will be helpful in future research. It is studied how the positivity of energy and entropy can impose additional restrictions on the domain of f (R, G$\mathcal{G}$) gravity. Moreover, a flat FLRW model corresponding to the f(R, G$\mathcal{G}$) theory will be considered and the related Friedman equations will be derived. The Cai‐Kim technique will then be used to evaluate the expression for energy flux passing through the horizon in insignificantly small time. In addition, the Clausius relation related to the evident boundary as well as the Cai‐Kim technique and the relating Friedmann equations will be used to find the expression for horizon entropy. [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]

This article investigates the physical features of static axial sources that produce complexity within the matter configuration within the perspective of f (R ,   T) theory, where R is the curvature invariant and T identifies the trace of matter energy tensor. In this case, the contracted Bianchi identities of effective as well as normal matter are used to develop the conservation equations. We split the curvature tensor to compute structure scalars, involving the physical aspects of the source in the influence of modified factors. We explore the evolving source and compute the complexity of the system. Three complexity factors are determined by using structure scalars; after that, the corresponding propagation equations are explored to investigate the intense gravitational consequences. Finally, the outcomes of irregular anisotropic spheroids are presented using the criterion of vanishing complexity. The f (R ,   T) corrections are shown to be an additional source of complexity for the axial anisotropic configuration. [ABSTRACT FROM AUTHOR]

This paper is asserted to explore the self-gravitating spherically symmetric anisotropic fluids in Chameleonic Brans–Dicke theory as dark energy matter. The dissipative and non-dissipative cases for the evolution of the system are discussed evidently satisfying the quasi-homologous condition with vanishing complexity (YTF) factor, which is identified in the trace free part of the electric Riemann tensor in splitting of the curvature tensor. We formulate different equations through conformal tensor, mass function, shear stress tensor, scalar field to govern self-gravitating systems. A few models describe center filled fluid distribution whereas some of them have cavities surrounding the center by means of matching conditions on the boundary as well as on inner surfaces. The temperature of the respective models is also discussed here. Finally, we conclude the work by comparing it with GR. [ABSTRACT FROM AUTHOR]

Through this study, we intend to present a comprehensive summary of the most recent research on complex systems or complexity factor ( f) in the background of modified gravity theories (MGT). In this way, we examined f for the novel MGT named f (, T 2) gravity under the anisotropic static fluid configuration. f is defined as one of the structure scalars (Y T F) which is trace-free component obtained from the orthogonal splitting of the Riemann tensor. Two mass approaches are used which have immense influence on f . Furthermore, vanishing complexity condition is used with an eye towards finding the solution of the nonlinear system. Two extra models are explored which ensure one more condition for the purpose of comprehensive 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]

This manuscript aims to establish the gravitational junction conditions for the f (G , T) gravity. In this gravitational theory, f is an arbitrary function of Gauss-Bonnet invariant G and the trace of the energy-momentum tensor T μ ν i.e., T. We start by introducing this gravity theory in its usual geometrical representation and posteriorly obtain a dynamically equivalent scalar-tensor representation on which the arbitrary dependence on the generic function f in both G and T is exchanged by two scalar fields and scalar potential. We then derive the junction conditions for matching between two different space-times across a separation hyper-surface Σ , assuming the matter sector to be described by an isotropic perfect fluid configuration. We take the general approach assuming the possibility of a thin-shell arising at Σ between the two space-times. However, our results establish that, for the distribution formalism to be well-defined, thin-shells are not allowed to emerge in the general version of this theory. We thus obtain instead a complete set of junction conditions for a smooth matching at Σ under the same conditions. The same results are then obtained in the scalar-tensor representation of the theory, thus emphasizing the equivalence between these two representations. Our results significantly constrain the possibility of developing models for alternative compact structures supported by thin-shells in f (G , T) gravity, e.g. gravastars and thin-shell wormholes, but provide a suitable framework for the search of models presenting a smooth matching at their surface, from which perfect fluid stars are possible examples. [ABSTRACT FROM AUTHOR]

This work aims to study the bouncing universe under f(G, T) theory of gravity (where G and T are the Gauss–Bonnet invariance and trace of energy–momentum tensor, respectively). We construct modified field equations (MFEs) to analyze the behavior of Hubble parameter (HP) for f (G , T) = G + α G n + 2 λ T with α , λ and (n > 0) are constant terms. Different constraints are applied, engaging HP to examine the accelerating universe and to test initial singularity. The graphical analysis is made for different values of n to explain bouncing process more precisely with respect to cosmic time that also provides an indication of null energy condition (NEC) violation. Resultantly, all mandatory conditions are fulfilled indicating that our proposed model provides good bouncing solutions. [ABSTRACT FROM AUTHOR]

This work investigates the effect of electromagnetic field on relativistic compact stellar structures coupled with anisotropic collapsing fluid under the framework of string‐motivated Gauss–Bonnet‐powered gravity. Using the power‐law form of Maxwell‐GB corrections, the stellar structure equations dubbed as Tolman–Oppenheimer–Volkoff (TOV) equations are developed. In the presence of a power‐law form of f(G)$f(\mathcal {G})$‐corrections, an evolution equation for the Weyl scalar is obtained, which plays a central role in the investigation of the examined fluid configuration. It is observed that the existence of shear in the fluid flow, irregularities in the distribution of energy density, dissipative fluxes, and modified Gauss–Bonnet corrections are the certain factors that are accountable for generating anisotropies in an originally isotropic fluid distribution. Some of the interesting consequences of formulated results are examined. This study investigates the effects of electromagnetic field on relativistic compact stellar structures coupled with anisotropic collapsing fluid. The results describe the evolving compact stellar structures with spherically symmetric background, which can prove to be more interesting as compared to the static configurations. This analysis is more attractive for studying the evolution of relativistic star configurations such as neutron stars as well as gravitational‐wave signals. [ABSTRACT FROM AUTHOR]

This work analyzes the dynamical variables and information transfer of a collapsing string fluid in the theory of Rainbow gravity (RG). Modifications are made to the field equations for the anisotropic string fluid in spherical geometry with the necessary rainbow functions. We have calculated the radius and time when effective horizons formed. This calculation helps to estimate the time of the observer reaching the apparent horizon. Moreover, we have computed the dynamical variables concerning the string fluid including mass density, pressure and the string tension. The behavior of the dynamical quantities is presented graphically. It is found that the rainbow parameter η affects the dynamical variables. The results enable us to understand the physics of a collapsing fluid and the information transfer in the collapsing scenario. [ABSTRACT FROM AUTHOR]

This paper deals with stability analysis of anisotropic-charged cylindrical geometry coupled with f (R , T) modified gravity theory (ℳ ). In this ℳ , the Lagrangian is a varying function of traces of Ricci and stress tensors. In order to examine the stable behavior of the anisotropic cylindrical cosmic object under the electromagnetic effects, we calculated the modified equations of motion and equations of continuity. in the background of f (R , T) theory. By utilizing the perturbation technique, we constitute a modified collapse equation (ℳ ℰ), which contains geometrical and physical variables in the charged scenario. Our investigation continues under the nonminimally coupled function of ℳ . Furthermore, we investigate the dynamically stable phases of charged geometry at Newtonian () and post-Newtonian (p ) epochs with the help of the rigidity parameter of fluid (Γ) by imposing some constraints on physical parameters. [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]

This paper is focused on the in/stability of a collapsing anisotropic self-gravitating spherically symmetric compact fluid under the influence of non-minimally coupled f(R, T) gravitational theory, where R and T are traces of Ricci tensor and stress-energy tensor, respectively. We explore the f(R, T) equations of motion as well as conservation equations. We utilize the perturbation technique on dynamical equations, and physical quantities to get the collapse equation in a similar scenario. In the presence of considered f(R, T)-function (i.e. f (R , T) = R − ζ R c tanh (R R c ) + λ R T), to explain the dynamical behavior of the considered anisotropic relativistic fluid system. Furthermore, to address the issue of in/stability, the conditions on adiabatic index Γ i.e. stiffness parameter of fluid, are developed for Newtonian (N) - e p o c h and post-Newtonian (p N) - e p o c h. Several physical constraints are imposed to maintain the un/stable fluid structure. [ABSTRACT FROM AUTHOR]

The objective of this paper is to investigate the continuation of Lemaître–Tolman–Bondi (LTB) space-time for dissipative dust configuration in the direction of Palatini f(R) theory. In this context, the generalized form of field and dynamical equations will be formulated. We explore the effects of kinematical variables and curvature invariant on our proposed fluid configuration. The significance of Palatini f(R) scalar variables computing through the orthogonal splitting of Riemann-tensor for dissipative dust spheres will be reported. Furthermore, two subcases of LTB space-time have been carried out to note down its symmetric aspects. It is revealed that extended LTB space-time has characteristics comparable to that of LTB and computed scalar variables in both situations have identical dependance on source profile even under the effects of Palatini technique. [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]

The aim of this manuscript is to explore singularity-free solution for a specific self-gravitating highly dense object known as gravastar suggested by Mazur and Mottola, in the context of f (G) gravity theory. Gravastars are regarded as a possible alternate to black hole. To derive modified field equations and law of conservation related to Gauss-Bonnet gravity, we assume cylindrically symmetric irrotational configuration. Particular equation of states are used for the illustration of three sectors of gravastar model. Furthermore, we are intended to obtain a regular solution for our model and graphs will be used to elaborate various substantial characteristics of it. [ABSTRACT FROM AUTHOR]

The concept of complexity for dynamical spherically symmetric dissipative self-gravitating configuration (Herrera et al. Phys. Rev. D, 98, 104059 (2018). doi:10.1103/PhysRevD.98.104059) is generalized in the scenario of modified Gauss–Bonnet gravity. For this purpose, a spherically symmetric fluid with locally anisotropic, dissipative, and non-dissipative configurations is considered. We choose the same complexity factor for the structure as we did for the static case, while we consider the homologous condition for the simplest pattern of evolution. In this approach, we formulate structure scalars that demonstrate the essential properties of the system. A fluid distribution that fulfills the vanishing complexity constraint and proceeds homologously corresponds to isotropic, geodesic, homogeneous, and shear-free fluid. In the dissipative case, the fluid is still geodesic but it is shearing, and there is a wide range of solutions. In the last, the stability of vanishing complexity is examined. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the stability constraints under the influence of particular modified gravity theory , i.e. f (R , T) gravity in which the Lagrangian is a varying function of R and trace of energy momentum tensor (T). We examine stable behavior for compact cylindrical star having anisotropic symmetric configuration. We establish dynamical equations as well as equations of continuity in the background of this particular non-minimal coupled . We utilize perturbation technique which will be applied on geometrical as well as material physical quantities to constitute collapse equation. We continue this significant investigation to understand the dynamical behavior of considered cylindrical system under non-minimal coupled f (R , T) functional, i.e. f (R , T) = R + ξ R c [ 1 − { 1 + R 2 R c 2 } − n ] + λ R T. This gravitational function gives compatible findings only for ξ > 0 , n ∈ R + , also 0 < λ ≪ 1 and λ R T considered in this astrophysical model as coupling entity. This model contains R c which is constant entity, having the values of order of the effective Ricci scalar R. Furthermore, we impose some physical constraints to determine and maintain the stability criteria by establishing the expression of adiabatic index, i.e. Γ for cylindrical anisotropic configuration, in Newtonian (N) and post-Newtonian (p N) eras. [ABSTRACT FROM AUTHOR]

This paper is dedicated to inspecting the appearance of electromagnetic field, which is caused by the presence of charge in the highly compact object named gravastar in the background of f (R , G) theory. According to conjecture introduced by Mazur and Mottola gravastar must be consisted of three sectors. We have interpreted these sectors by using specific equations of states. Spherically static metric, perfect fluid and the isotropic pressure have been used in order to calculate a singularity free solution. Gravitational mass present in the inner sector of gravastar is changed into electromagnetic mass in the existence of charge. The electromagnetic mass model of inner sector is responsible for stability by providing balance to the repulsive pressure, which is caused by the presence of charge. It is observed that the presence of electrical charge has a significant effect on energy content, entropy and proper length of the shell that is demonstrated with the help of graphs. [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]

The principal idea behind this manuscript is to inspect the complexity of dissipating as well as non-dissipating self-gravitating sources which are coupled with locally anisotropic charged matter. The gravitational equations in the regime of |$f(\mathbb {G})$| (⁠|$\mathbb {G}$| is the Gauss–Bonnet invariant) theory have elaborated for the imperfectly charged stellar configuration to scrutinize the charged object in the presence of |$f(\mathbb {G})$| corrections. The impact of charge distribution on the connection between density inhomogeneity, Weyl tensor, and pressure anisotropy is investigated. By incorporating the constraints of Q H (i.e. the quasi-homologous) evolution and C F = 0, (where C F denotes the complexity factor) multiple analytical solutions to the |$f(\mathbb {G})$| equations of gravity are developed defining the imperfectly charged compact spherical matter. Some of these stellar models (exact solutions) portray a spherical collapsing configuration of a charged fluid in which there arise a cavity about the fluid centre, while other models exhibit a fluid configuration wherein the sphere is totally filled by the fluid. These interior solutions to |$f(\mathbb {G})$| gravitational equations may exhibit some appealing astrophysical phenomenons. [ABSTRACT FROM AUTHOR]

The objective of this article is to investigate the effects of electromagnetic field on the generalization of Lemaître–Tolman–Bondi (LTB) spacetime by keeping in view the Palatini f(R) gravity and dissipative dust fluid. For performing this analysis, we followed the strategy deployed by Herrera et al. (Phys Rev D 82(2):024021, 2010). We have explored the modified field equations along with kinematical quantities and mass function and constructed the evolution equations to study the dynamics of inhomogeneous universe along with Raychauduary and Ellis equations. We have developed the relation for Palatini f(R) scalar functions by splitting the Riemann curvature tensor orthogonally and associated them with metric coefficients using modified field equations. We have formulated these scalar functions for LTB and its generalized version, i.e., GLTB under the influence of charge. The properties of GLTB spacetime are consistent with those of the LTB geometry and the scalar functions found in both cases are comparable in the presence of charge and Palatini f(R) curvature terms. The symmetric properties of generalized LTB spacetime are also studied using streaming out and diffusion approximations. [ABSTRACT FROM AUTHOR]

In this paper, we discuss various analytical solutions of the planner geometry with anisotropic fluid as well as vanishing complexity factor condition in the framework of f(픾) theory. The matching conditions are employed at the interior and exterior hypersurfaces. The connection between the matter parameters and the Weyl tensor has been constructed. For dissipative and non-dissipative structures, we examine four different conformal Killing vector possibilities, while some possibilities adhere to the 풴TF = 0 condition along with the matching conditions, where 풴TF indicates the trace free part of the electric component of the Riemann tensor. Several theoretical models are provided to show how a non-static system evolves. [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]

We consider the definition of complexity for dynamical spherically self-gravitating matter distribution in the presence of heat dissipation introduced by Herrera [L. Herrera, A. Di Prisco and J. Ospino, Phys. Rev. D 98 (2018) 104059] and generalize it in f (R , T , R μ ν T μ ν) gravity, where R and T are the Ricci scalar and the trace of energy–momentum tensor, respectively. We measure the complexity of structure as well as pattern of evolution of the fluid distribution and examine these under the effects of dark source terms of modified gravity. Some dynamical and kinematical equations are observed in the dissipative and nondissipative cases in the background of modified theory. Finally, we discuss evolution of the structure scalars and stability of a condition where the complexity factor vanishes. [ABSTRACT FROM AUTHOR]

This paper explores spherically symmetrical dynamical traversable wormhole solutions for an anisotropic fluid configuration in the context of f(R) gravity. We construct the corresponding field equations and investigate the wormhole solutions by specifying the redshift and shape functions for three models of f(R) gravity. Graphical analysis shows that ordinary matter satisfies the null as well as weak energy conditions against the time and radial coordinates for each model. It is concluded that dynamical traversable wormholes are supported by this theory. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the effects of shear viscosity on a dissipative spherical collapse in the presence of heat dissipation and anisotropic pressure. In the background of f (R , T , Q) gravity, where R is Ricci scalar, T constitutes the trace of energy–momentum tensor, and Q ≡ R μ ν T μ ν , we examine the particular role of shear viscosity on the dynamical equations, and couple it with the heat transport equation, which is interpreted by Israel–Stewart theory. We reacquire the reduction in the inertial mass density of the matter with the addition of viscosity terms, by a factor (1 − α) which depends upon the inner states of thermodynamics. With the conformity of the equivalence relationship, the decline in inertial density is very close to gravitational force. To determine the particular results, we construct a relationship of Weyl tensor with distinctive matter variables. We study the inhomogeneous characteristics of energy density in this scenario and examine the significant effects of modified gravity along with shear viscosity. [ABSTRACT FROM AUTHOR]

In this paper, we have studied the stability of neutron stars in the background of Palatini f(R, T) gravity. In this context, the static spherically symmetric geometry is considered which is assumed to be coupled with an isotropic matter configurations. The evolution of the system is considered with the help of Tolman–Oppenheimer–Volkoff equations and conformal transformations. We found the stable configurations of the spherical stars with some constraints. [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]

In this work, we discuss the stability of charged neutron star in the background of f (R ̂) gravity and construct the generalized Tolman–Oppenheimer–Volkoff (TOV) equations. For this, we consider static spherically symmetric geometry to construct the hydrostatic equilibrium equation and deduce TOV equations from modified field equations with electromagnetic effects. We conclude that the generalized TOV equation depicts the stable stars configuration independent of the generic function of the modified gravity if the condition of uniform entropy and chemical composition is assumed. [ABSTRACT FROM AUTHOR]

This paper deals with the exploration of collapse rate and Tolman mass function for spherical system under the influence of f (R) modified gravity theory after using Herrera technique. We have taken the matter configuration to be anisotropic as well as dissipative due to diffusion and streaming out radiations. The modified field equations and dynamical equations are explored for a systematic investigation of Tolman mass. An explicit link among the matter profile, Weyl tensor and mass function is exhibited in this scenario. We found that the anisotropic pressure and density inhomogeneity tends to increase the Tolman mass within the sphere radius, while f (R) terms stabilize the system. [ABSTRACT FROM AUTHOR]

The aim of this paper is to investigate the influence of expansion-free condition and cosmological constant in the modeling of planar relativistic self-gravitating objects. For this purpose, we have considered a non-static diagonally oriented planar geometry that is coupled with locally anisotropic non-radiating matter configurations. Firstly, we have explored the factor responsible for maintaining conformal flat state by relating tidal forces with matter dynamical variables. Then, we have smoothly joined our relativistic interior with the exterior one through Darmois junction conditions in the Λ -dominated epoch. We have also shown that the well-known perfect fluid Skripkin model has disobeyed matching conditions for the case of planar system with cosmological constant. Lastly, we have inspected family of exact analytical solutions of Einstein- Λ field equations with various backgrounds, like, an/isotropic matter, separable energy density and barotropic equation of state. [ABSTRACT FROM AUTHOR]

In this paper, we examined the viability bounds of a higher derivative f ( R , □ R , T ) theory through analyzing energy conditions (where R , □ R and T are the Ricci scalar, d’Alemberts operator and trace of energy–momentum tensor, respectively). We take flat Friedmann–Lemaître–Robertson–Walker spacetime coupled with ideal configurations of matter content. We consider three different realistic models of this gravity, that could be utilized to understand the stability of cosmological solutions. After constructing certain bounds mediated by energy conditions, more specifically the weak energy condition, we discuss viable zones of the under considered modified models in an environment of recent estimated numerical choices of the cosmic parameters. [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]

The goal of this paper is to shed some light on the significance of congruence of observers, which seems to affect the dynamics of the universe under Palatini f( R) formalism. Starting by setting up the formalism needed, we have explored the field equations using Lemaitre-Tolman-Bondi geometry as an interior metric. We have formulated the relationship between the matter variables as seen by the observers in both co-moving and non-co-moving frames. The dynamical equations are evaluated to study the dynamics of inhomogeneous universe by exploring conservation equations along with the Ellis equations. We have also explored a collapsing factor describing the bouncing phenomena via transport equation and conclude the stability region. [ABSTRACT FROM AUTHOR]

This paper explores some wormhole (WH) solutions in the background of additional matter contents of f( R, T) modified gravity. For this purpose, we have considered WH geometry filled with two physically different fluid configurations: one is anisotropic and another is anisotropic characterized by the barotropic equation of state. The energy conditions are examined with particular modified gravity model and found the existence of WH solutions even in the absence of exotic matter. Also, we have analyzed the behavior of shape function in this framework. The stability and physical existence of these solutions is studied with different fluid configurations. We conclude that in the absence of exotic matter, one can find WH solutions with particular model of modified gravity. [ABSTRACT FROM AUTHOR]

In this paper, we explore the possibility for the existence of thin-shell wormholes for the charged black string in the framework of f ( R ) gravity theory. We have carried out our analysis by keeping linear perturbations about static equilibrium solutions where we have surgically pasted the interior spacetime to an exterior vacuum geometry. We have assumed logarithmic as well as exponential form of well-known f ( R ) models and investigated their role in the modeling of stable/unstable thin-shell wormholes. As a specific case, we perform our analysis through distributions of mass, charge and equation of state parameter. We found that various static thin-shell wormhole backgrounds are possible for different parametric values of f ( R ) models. We also concluded that modified gravity induced by logarithmic and exponential f ( R ) models could likely to host wide range of wormholes. [ABSTRACT FROM AUTHOR]