Narrow Results

In this paper, we explore a comprehensive analysis of the formalism governing the gravitational field equations in degenerate higher-order scalar–tensor theories. The propagation of these theories in the vacuum has a maximum of three degrees of freedom and is at most quadratic in the second derivative of the scalar field. We investigate the gravitational field equation for spherically symmetric anisotropic matter content along with its non-conserved equations. Our analysis focuses on the evaluation of structure scalars to assess their behavior under Einstein’s modification. We present a realistic mass contribution that sheds light on both geometric mass and total energy budget evaluations for celestial objects. Ultimately, we discuss two viable models restricted as minimal complexity and conformal flatness to enhance the scientific contribution of this paper.

This research paper aims to redefine the complexity factor in $f(R,G)$ gravity and the appearance of electric charge, where $R$ is the Ricci scalar and $G$ is the Gauss–Bonnet term. In this context, we intend to analyze the splitting of the Riemann tensor after considering the anisotropic distribution of the charged fluid related to the spherically symmetric spacetime. We interpret $Y_{\mathrm{\text{TF}}}$ as the complexity factor among all the determined structural scalars that encompasses the characteristics of anisotropic pressure and the effective representation of the energy density. The correction terms associated with modified theory are considered to calculate some significant results related to the Weyl scalar, Tolman mass, and the complexity factor (CF). Moreover, the expression for CF is established by using the structure scalars determined in our paper, and the diminishing complexity restraint is utilized to determine the solutions for the various models. The celestial object having non-uniform energy density and anisotropic pressure asserts the maximum intricacy. But, if the effects of non-uniform energy density and anisotropic distribution of pressure are eradicated due to the presence of dark source terms associated with modified gravity then these fluids may not exhibit any complexity. Consequently, it is revealed that the constituents of effective and electromagnetic parts directly influence the structure scalars and CF.

We consider non-adiabatic flow of the fluid possessing dissipation in the form of shearing viscosity in electromagnetic field. The scalar functions (structure scalars) for charged plane symmetry are formulated and are related with the physical variables of the fluid. We also develop a relationship between the Weyl tensor and other physical variables by using Taub mass formalism. The role of electric charge as well as its physical significance for the evolution of the shear tensor and expansion scalar are also explored. Finally, we discuss a special case for dust with cosmological constant.

One of the striking feature of inhomogeneous matter distribution under the effects of fourth-order gravity and electromagnetic field have been discussed in this manuscript. We have considered a compact spherical celestial star undergoing expansion due to the presence of higher curvature invariants of $f(R)$ gravity and imperfect fluid. We have explored the dynamical equations and field equations in $f(R)$ gravity. An explicit expression have been found for Weyl tensor and material variables under the dark dynamical effects. Using a viable $f(R)$ model, some dynamical variables have been explored from splitting the Riemann curvature tensor. These dark dynamical variables are also studied for charged dust cloud with and without the constraint of constant Ricci scalar.

This paper investigates the effects of dark source term on the dissipative axially symmetric collapse by taking self-interacting Brans–Dicke (SBD) gravity as a dark energy (DE) candidate. We discuss physically feasible energy source of the model and formulate all the dynamical variables as well as structure scalars. It is found that the dark source term is one of the source of anisotropy and dissipation in the system. Further, we obtain structure scalars in this background. In order to discuss factors describing dissipative collapse, we develop equations related to the evolution of dynamical variables, heat transport equation as well as super-Poynting vector. We conclude that the thermodynamics of the collapse, evolution of kinematical terms (like expansion scalar, shear and vorticity) and inhomogeneity are affected by dark source term. Finally, we study the existence of radiation having repulsive gravitational nature in this collapse scenario.

This paper explores evolution of dissipative axially symmetric collapsing fluid under the dark effects of $f(G)$ gravity. We formulate the dynamical variables and study the effects of dark sources in pressure anisotropy as well as heat dissipation. The structure scalars (scalar functions) as well as their role in the dynamics of source are investigated. Finally, we develop heat transport equation to examine the thermodynamic aspect and a set of equations governing the evolution of dynamical variables. It is concluded that dark sources affect thermodynamics of the system, evolution of kinematical quantities as well as density inhomogeneity.

In this paper, we analyze some dynamical features of spherical celestial objects through structure scalars in $f(R,T)$ gravitational theory, where $R$ and $T$ are the Ricci scalar and the trace of energy–momentum tensor, respectively. In this framework, we consider our relativistic geometry to be spherical in shape filled with radiating viscous and shearing fluid content. We formulate extended version of structure scalars by orthogonal decomposition of the Riemann tensor with and without constant $R$ and $T$ backgrounds. We discuss the effects of dark source corrections on the construction of expansion and shear evolution equations via scalar variables. It is inferred that like general relativity, one can investigate the evolutionary stages of stellar compact objects with the help of extended scalar parameters.

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.

The main goal of this paper is to present the Lemaître–Tolman–Bondi (LTB) spacetime for the radiating case by extending the study of [L. Herrera, A. Di Prisco, J. Ospino and J. Carot, Phys. Rev. D 82 (2010) 024021] in $f(R,T)$ theory, where $R$ is the Ricci scalar and $T$ is the energy–momentum tensor trace. We will start with some fundamental equations, such as the kinematical variables, mass function introduced by Misner and Sharp, the Weyl tensor under the influence of the $f(R,T)$ modified Bianchi identities. We have also considered the evolution of the modified constraint equation. Later on, we have analyzed LTB in terms of modified structure scalars emerging from the orthogonal splitting of the Riemann tensor, and the transport equation in $f(R,T)$ gravity theory. We will also discuss a case in order to generalize LTB metric.

The motive of this paper is to investigate the evolution of dissipative axially symmetry collapsing fluid in the presence of dark sources. For this purpose, we use the modified Gauss–Bonnet gravity as an exotic energy candidate. We formulate the dynamical variables and investigate the impacts of dark sources upon the heat dissipation and pressure anisotropy. We find scalar functions through orthogonal decomposition of Riemann tensor. The physical behavior of these scalars has been examined for matter as well as dark source configurations. Moreover, we develop a set of EEs related to the evolution of dynamical variables, heat transport equation, Weyl tensor and super-Poynting vector. These equations discuss collapse features like thermodynamics, density inhomogeneity and gravitational radiations in presences of exotic terms. It has been shown that the dark source terms have an effect on the thermodynamics of the system, evolution of kinematical variables and density inhomogeneity. The exotic terms can generate repulsive radiations which can induce cosmic expansion. Finally, the physical significance of modified Gauss–Bonnet gravity is explored in association to the stellar 4U1820-30.

Through this study, we intend to present a comprehensive summary of the most recent research on complex systems or complexity factor $({{𝒞}}_f)$ in the background of modified gravity theories (MGT). In this way, we examined ${{𝒞}}_f$ for the novel MGT named $f({𝒢},T^2)$ gravity under the anisotropic static fluid configuration. ${{𝒞}}_f$ is defined as one of the structure scalars $(Y_{TF})$ which is trace-free component obtained from the orthogonal splitting of the Riemann tensor. Two mass approaches are used which have immense influence on ${{𝒞}}_f$. 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.

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.

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 $Y_{\mathrm{\text{I}}}$, $Y_{\mathrm{\text{II}}}$ and $Y_{\mathrm{\text{KL}}}$ 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.

In this paper, we present 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 modified version of Ellis equations. We explore different factors responsible for energy density inhomogeneities with non-dissipative dust, isotropic and dissipative dust cloud.