Narrow Results

This paper is devoted to studying the structure of gravitationally vacuum condensate stars under the influence of matter and geometry coupled gravity. This alternative to black hole comprises three domains, i.e. interior, exterior and thin-shell. We investigate such regions by considering particular equations of state for a specific model of energy–momentum squared gravity. The nonsingular solutions of field equations are obtained to describe the interior region of gravastar and the Schwarzschild spacetime represents the exterior region. The junction conditions are used to match interior and exterior domains while Lanczos equations provide the surface density and pressure at thin-shell. We investigate various attributes of gravastar such as the equation of state parameter, entropy, proper length as well as energy. The physical features of a gravitationally vacuum star indicate a linear relationship with the thickness of the shell and provide a viable structure similar to general relativity.

This paper examines the structure of a gravitational vacuum star (also known as gravastar) in the background of $f(\Re ,{{𝒯}}^2)$ theory. This hypothetical object can be treated as a substitute of a black hole, with three regions: (i) the internal region, (ii) the intrinsic shell and (iii) the outer region. We examine these geometries using Finch–Skea metric for the radial metric component along with the particular $f(\Re ,{{𝒯}}^2)$ model. We determine singularity-free solutions for both the inner as well as thin-shell domains. The smooth matching of the interior region with external Schwarzschild spacetime is obtained through Israel matching constraints. Finally, we study various characteristics of gravastar domains including the equation-of-state parameter, proper length, entropy, energy as well as surface redshift. It is found that the compact gravastar structure is a viable alternate to the black hole in the perspective of this gravity.

This paper is dedicated to the precise computation of anisotropic extensions for the Tolman IV solution. These extensions are achieved through the utilization of the extended gravitational decoupling scheme within the framework of $f(R,T^2)$ gravity, where R is the Ricci scalar and $T^2$ is the contraction of energy–momentum tensor. In this context, we select a linear model characterized by the expression $f(R,T^2)=R+\xi T^2$, where the parameter $\xi$ establishes a connection between the geometric and matter components. The extended gravitational decoupling technique incorporates a decoupling parameter that governs the extent of the induced anisotropy. Deformations in the radial and temporal metric components lead to the decomposition of the field equations into two distinct subsystems. One of these sets pertains to the isotropic solution, while the other is addressed by implementing the extra constraints. We examine the outcomes through graphical analysis and investigate the viability and stability of the obtained anisotropic solutions for the celestial object. Moreover, we study the mass, compactness and surface redshift of the system to gain a comprehensive understanding of its characteristics. It is concluded that this technique in this modified gravity yields physically acceptable solutions.

In this paper, we investigate how the electromagnetic field influences the idea of complexity within the framework of squared gravity. The physical traits, including heat dissipation, charge, anisotropic pressure, energy density variations and correction components are found to be significant contributors of complexity in celestial objects. By employing Herrera’s orthogonal splitting approach, scalar functions are obtained yielding a complexity factor that incorporates the crucial attributes of the self-gravitating system. Furthermore, we examine the dynamics of charged spherical configuration by considering homologous mode as the simplest evolutionary pattern. Our investigation includes complexity-free scenarios (dissipative/non-dissipative) with homologous constraints. Moreover, we explore the components that contribute toward complexity during the evolutionary process. We conclude that self-gravitating structures get more complex with the inclusion of extra curvature terms of squared gravity and charge.

This paper examines the behavior of the universe around the bouncing point in the background of $f(\mathcal{𝒬},\mathcal{𝒯})$ theory, where $\mathcal{𝒬}$ is the non-metricity and $\mathcal{𝒯}$ is the trace of the energy–momentum tensor. We derive the field equations that describe gravitational phenomena in the existence of non-metricity and matter source terms. By applying the reconstruction method for the Hubble parameter, a phenomenon of the bouncing universe for homogeneous spacetime filled with perfect fluid is studied. We consider specific models of this modified theory to evaluate the behavior of various cosmic parameters such as the Hubble, deceleration, equation of state and fluid parameters. When the null energy condition is violated, it follows a bouncing behavior. It is found that spacetime is composed of isotropic fluid, where a big bounce can occur and the universe turns into extremely unstable. We conclude that $f(\mathcal{𝒬},\mathcal{𝒯})$ gravity successfully explains the early and late time cosmic expansion and evolution.

In the bibliography, a certain confusion arises in what regards to the classification of the gravitational theories into scalar–tensor theories (STT) and general relativity with a scalar field either minimally or nonminimally coupled to matter. Higher-derivatives Horndeski and beyond Horndeski theories that at first sight do not look like STT only add to the confusion. To further complicate things, the discussion on the physical equivalence of the different conformal frames in which a given scalar–tensor theory may be formulated, makes even harder to achieve a correct classification. In this paper, we propose a specific criterion for an unambiguous identification of STT and discuss its impact on the conformal transformations issue. The present discussion carries not only pedagogical but also scientific interest since an incorrect classification of a given theory as a scalar–tensor theory of gravity may lead to conceptual issues and to the consequent misunderstanding of its physical implications.

This paper examines the structure of gravastar (gravitationally vacuum star) in the background of $f(\Re ,{{𝒯}}^2)$ theory. The gravastar can be regarded as a substitute for a black hole comprising of three regions (i) the interior domain, (ii) the intrinsic shell and (iii) the exterior domain. We investigate these domains by employing Karmarkar’s condition by assuming a specific $f(\Re ,{{𝒯}}^2)$ model. The field equations are solved to evaluate nonsingular solutions of both the interior and intermediate regions. Inner as well as outer spacetimes are matched together using Israel formalism to obtain density and pressure at the joining surface. Different attributes of gravastar like the equation of state parameter, proper length, entropy and energy are analyzed through graphical behavior. It is found that the gravastar model is a viable alternative to the black hole in the context of this gravity.

This paper investigates the possibility of reconstruction of the generic function in $F({ℛ},T)$ gravitational theory by considering some well-known cosmological bouncing models, namely, exponential evaluation, oscillatory, power law and matter bounce model, where ${ℛ}$ and $T$ are Ricci scalar and trace of energy–momentum tensor, respectively. Due to the complexity of dynamical field equations, we propose some ansatz forms of function $F({ℛ},T)$ in perspective models and examine which type of Lagrangian is capable of reproducing bouncing solution via analytical expression. It is seen that for some cases of exponential, oscillatory and matter bounce models, it is possible to get analytical solution while in other cases, it is not possible to achieve exact (general) solutions so only complementary solutions can be discussed. However, for power-law model, all forms of generic function can be reconstructed analytically. Next we analyze the energy conditions and stability of these reconstructed cosmological bouncing models which have analytical forms. It is found that these models are stable for linear forms of Lagrangian only but the reconstructed solutions for power law are unstable for some nonlinear forms of Lagrangian. Further, we determine the observable quantities like spectral index ($n_s$) and tensor-to-scalar ratio ($r$) for the simplest reconstructed form of $f(R,T)$ function. As a result, we directly confront the reconstructed linear form of Lagrangian in $F({ℛ},T)$ model with 2018 Planck observations. Furthermore, we analyze that $F({ℛ},T)$ gravity with dark energy epoch is consistent with Sne-Ia+BAO+H(z)+CMB data and show that bounce can unify with dark energy epochs in $F({ℛ},T)$ gravity.

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.

To make a comparison of energy conditions in the theory of general relativity and in the modified theories, we have considered $f(R)$, $f(R,T)$ and $f(R,T,Q)$ theories (where $R$ and $T$ are the Ricci scalar and trace of the energy–momentum tensor, respectively, while $Q=T^{ab}{R}_{ab}$) to test the validity of all the four energy conditions. These energy conditions had been derived to check the viability of cosmological as well as astrophysical models. In this paper, we consider the standard Friedmann–Robertson–Walker spacetime representing the homogeneous and isotropic universe, and investigate the available literature on testing energy conditions as well as calculate these conditions ourselves. In order to provide the comparative results, we test these conditions analytically as well as graphically and present how energy bounds in modified theories depend on the values of the involved parameters and its validity within certain limits. We discuss here, that which of the modified theories comply with certain energy conditions, and hence provide a supporting argument on the existence of modified theories.

This paper explores the existence of static wormholes in 4-Dimensional Einstein Gauss–Bonnet (4D EGB) gravity. We discuss some possibilities for constructing radial-dependent shape functions via different strategies to develop some non-conventional wormhole geometries by considering anisotropic matter sources. In this regard, we assume a specific form of the equation of state and investigate its effects on Gauss–Bonnet (GB) coupling parameter. Next, we impose a traceless condition on the anisotropic fluid distribution as well as radial-dependent energy density profile to explore wormhole geometries as separate cases. It is seen that the obtained results can be reduced into Morris–Throne wormholes for the zero value of GB-coupled parameter for anisotropic fluid distribution. Furthermore, we scrutinize flaring-out conditions and examine asymptotically flatness constraints for the existence of wormholes. Our analysis shows that the weak energy condition (WEC) is satisfied for a particular range by constraining GB-coupled parameter. We study the dynamics of GB-coupled parameter for both cases $\mu >0$ and $\mu <0$. It is concluded that wormhole solutions are possible for $\mu >0$ and, in some cases, $\mu <0$. The active gravitational mass of developed wormholes is calculated and plotted graphically. The wormhole geometry is discussed by plotting 2D and 3D embedding diagrams. In order to analyze the complexity of the system, we have plotted the complexity factor for each wormhole.

We consider a gravitational theory that contains the Einstein term, a scalar field and the quadratic Gauss-Bonnet term. We focus on the early-universe dynamics, and demonstrate that the Ricci scalar does not affect the cosmological solutions at early times, when the curvature is strong. We then consider a pure scalar-GB theory with a quadratic coupling function: for a negative coupling parameter, we obtain solutions that contain always an inflationary, de Sitter phase, while for a positive coupling function, we find instead expanding singularity-free solutions.