Designing wormholes in novel power-law f(R): a mathematical approach with a linear equation of state

In this study, we search for a new class of wormhole solutions in the framework of Brans–Dicke (BD) theory in the presence of anisotropic matter distribution. Considering a linear equation of state (EoS) between radial pressure and energy density profile we find exact static spherically symmetric solutions to the BD field equations which represent wormhole configurations. The solutions we obtain include both cases with zero and nonzero redshift functions, for which, the conditions on wormhole geometry together with the weak (WEC) and null (NEC) energy conditions put constraints on model parameters such as, the BD coupling and EoS parameters. These constraints also depend on other model parameters such as, the value of BD scalar field and energy density at the wormhole throat. The regularity of the obtained solutions is verified by calculating the Kretschmann scalar in order to ensure that curvature singularities are absent in the wormhole spacetime. We then find that BD wormholes in the presence of anisotropic matter can exist without violating NEC and WEC, either at the throat or across the entire spacetime.

We have constructed a dark energy cosmological model in the framework of the generalized Brans Dicke (GBD) theory with a self-interacting potential. The source of dark energy is considered through a unified dark fluid (UDF) characterized by a linear equation of state (EoS). A time-varying deceleration parameter simulating the cosmic transit behavior has been introduced to get the dynamical behavior of the model. The $$H(z)$$ data have been explored to constrain the model parameters and to study the dynamical aspects of the Brans-Dicke parameter and the scalar field.

General Relativistic Stars: Linear Equations of State

A Bianchi type-V space time is considered with linear equation of state in the scalar tensor theory of gravitation proposed by Brans and Dicke. We use the assumption of constant deceleration parameter and power law relation between scalar field o and scale factor R to find the solutions. Some physical and kinematical properties of the model are also discussed.

Models of static wormholes within the [Formula: see text] extended theory of gravity are investigated, in particular the family [Formula: see text], with [Formula: see text] being the trace of the energy–momentum tensor. Models corresponding to different relations for the pressure components (radial and lateral), and several equations-of-state (EoS), reflecting different matter content, are worked out explicitly. The solutions obtained for the shape functions of the generated wormholes obey the necessary metric conditions, as manifested in other studies in the literature. The respective energy conditions reveal the physical nature of the wormhole models thus constructed. It is found, in particular, that for each of those considered, the parameter space can be divided into different regions, in which the exact wormhole solutions fulfill the null energy conditions (NEC) and the weak energy conditions (WEC), respectively, in terms of the lateral pressure. Moreover, the dominant energy condition (DEC) in terms of both pressures is also valid, while [Formula: see text]. A similar solution for the theory [Formula: see text] is found numerically, where [Formula: see text] and [Formula: see text] are either constant or functions of [Formula: see text], leading to the result that the NEC in terms of the radial pressure is also valid. For nonconstant [Formula: see text] models, attention is focused on the behavior [Formula: see text]. To finish, the question is addressed, how [Formula: see text] will affect the wormhole solutions corresponding to fluids of the form [Formula: see text], in the three cases such as NEC, WEC and DEC. Issues concerning the nonconservation of the matter energy–momentum tensor, the stability of the solutions obtained, and the observational possibilities for testing these models are discussed in Sec. 6.

Rastall theory propounded some five decades ago belongs to a class of modified theories of gravity. Such theories are motivated by the need to modify general relativity suitably in order to address some problems not explained by the standard theory. Amongst such issues are the observed accelerated expansion of the universe, motion in extremely high gravity regimes and explanations for the discrepancy in the value of the cosmological constant between quantum gravity and experimentation. Recently, it has been claimed that the Rastall theory is trivially equivalent to the standard Einstein theory. We investigate this claim in the context of stellar structure and elementary requirements for physical plausibility. We consider the analogue of the Saslaw et al. [Astrophys. J. 471, 571 (1996)] isothermal model of general relativity and show that the Rastall version satisfies the basic requirements unlike its counterpart. Then, we examine in turn the consequences of suppressing one of the inverse square law fall off of the energy density or the linear equation of state. Imposing a linear barotropic equation of state, we find a generalized de Sitter spacetime as an exact solution of the Rastall equations. In addition, the case of a constant spatial gravitational potential is studied. In each case, we note that the physics of the Rastall model differs from that of the Einstein version.

Compact anisotropic stellar distribution with linear barotropic equation of state in energy–momentum trace coupling modification of general relativity

This study aims to investigate spherically symmetric anisotropic solutions that describe compact stellar objects in the modified Rastall teleparallel (MRT) theory of gravity. In order to achieve this goal, we utilize the Karmarkar condition to evaluate the spherically symmetric components of the line element. We explore the field equations by selecting appropriate off-diagonal tetrad fields for two different scenarios. In the first scenario, we use a hybrid form of f(T)=βemTTn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T)=\\beta e^{m T} T^n$$\\end{document} and a linear equation of state (EoS) pr=ξρ+ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_r=\\xi \\rho +\\phi $$\\end{document}, where 0<ξ<1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0< \\xi < 1$$\\end{document}, to evaluate h(T). In the second scenario, we again use a hybrid form of f(T)=βemTTn\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(T)=\\beta e^{m T} T^n$$\\end{document} and a logarithmic form of h(T)=ψlog(ϕTχ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$h(T)=\\psi \\log (\\phi T^{\\chi })$$\\end{document}. We aim to investigate the possible forms of gravity modifications by evaluating the function for different values of m and n, reducing the gravity forms to hybrid, power law form, and exponential form. Our findings reveal that the exponential-logarithmic case is unstable in our scenario. To the best of our knowledge, we are the first to attempt to explore compact star models in MRT gravity. After obtaining the field equations, we investigate different physical parameters that demonstrate the stability and physical acceptability of the stellar models. We utilize observational data, such as the mass and radius of the PSRJ1416-2230\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$PSRJ\\;1416-2230$$\\end{document} model, to ensure the physical plausibility of our findings.

Our present study involves the strange stars model in the framework of $f(R,T)$ theory of gravitation. We have taken a linear function of the Ricci scalar $R$ and the trace $T$ of the stress-energy tensor $T_{\mu \nu}$ for the expression of $f(R,T)$, i.e., $f(R,T)=R+ 2 \gamma T $ to obtain the proposed model, where $\gamma$ is a coupling constant. Moreover, to solve the hydrostatic equilibrium equations, we consider a linear equation of state between the radial pressure $p_r$ and matter density $\rho$ as $p_r=\alpha \rho-\beta$, where $\alpha$ and $\beta$ are some positive constants, Both $\alpha,\,\beta$ depend on coupling constant $\gamma$ which have been also depicted in this paper. By employing the Krori-Barua {\em ansatz} already reported in the literature [J. Phys. A, Math. Gen. 8:508, 1975] we have found the solutions of the field equations in $f (R, T )$ gravity. The effect of coupling constant $\gamma$ have been studied on the model parameters like density, pressures, anisotropic factor, compactness, surface redshift, etc. both numerically and graphically. A suitable range for $\gamma$ is also obtained. The physical acceptability and stability of the stellar system have been tested by different physical tests, e.g., the causality condition, Herrera cracking concept, relativistic adiabatic index, energy conditions, etc. One can regain the solutions in Einstein gravity when $\gamma\rightarrow 0$

A mistake in calculation has been corrected and new references have been added

In this paper, we investigate the charged static spherically symmetric models in [Formula: see text] theory of gravity. We consider a linear equation of state (EoS) in the background of anisotropic matter configuration. We formulate the modified field equations and implement Durgapal transformation to examine the gravitational nature of compact stellar objects. For this purpose, we choose a specific gravitational potential and electric charge intensity to analytically solve the set of field equations. We generate three special cases of solutions for specific parametric values of [Formula: see text] appearing in the expression of gravitational potential. The evolution of physical observables, such as energy density, anisotropy parameter, radial and tangential pressures and electric field intensity, are presented in all cases. Via physical analysis, it is observed that the solution of charged compact spheres satisfies acceptability criteria, models are well behaved, and depict stability and consistency in accordance with [Formula: see text] gravity for generated models.

This analysis explores the new wormhole (WH) solution in the background of teleparallel gravity with minimal matter coupling. To complete this study, we consider the conformal symmetry with non-zero Killing vectors. The exact shape function is computed by considering the linear equation of state with the phantom regime. The energy conditions are investigated for the calculated shape function with the equation of state parameter. The presence of exotic matter is confirmed due to the violation of the null energy condition. The current study also explores the physical properties of the epicyclic frequencies with quasi-periodic oscillations. In the astrophysical, epicyclic frequencies are extensively employed to explore the self-gravitating system. It is concluded that a stable WH solution is acceptable for WH geometry.

In this study, we obtain wormhole solutions in the recently proposed extension of symmetric teleparallel gravity, known as gravity. Here, the gravitational Lagrangian L is defined by an arbitrary function f of Q and T, where Q is a non-metricity scalar, and T is the trace of the energy-momentum tensor. In this study, we obtain field equations for a static spherically symmetric wormhole metric in the context of general gravity. We study the wormhole solutions using (i) a linear equation of state and (ii) an anisotropy relation. We adopt two different forms of , (a) linear and (b) non-linear , to investigate these solutions. We investigate various energy conditions to search for preservation and violation among the obtained solutions and find that the null energy condition is violated in both cases of our assumed forms of . Finally, we perform a stability analysis using the Tolman-Oppenheimer-Volkov equation.

In this paper, we study the -gravitation theory under the assumption that the standard matter-energy content of the universe is a perfect fluid with linear barotropic equation of state within the framework of Bianchi-Type III model from the class of homogeneous and anisotropic universe models. However, whether such a restriction lead to any contradictions or inconsistencies in the field equations will create an issue that needs to be examined. Under the effective fluid approach, we will be concerned mainly the field equations in an orthonormal tetrad framework with an equimolar and examined the situation of establishing the functional form of together with the scale factors, which are their solutions. Unlike similar studies, which are very few in the literature, instead of assuming preliminary solutions, we determined the consistency conditions of the field equations by assuming the matter energy content of the universe as an isotropic perfect fluid for Bianchi-Type III.

Acharya and Hogan (1973) have introduced a massive scalar field into the usual Brans-Dicke (1961) theory of gravitation. Formally they obtain certain field equations. The assumption of a nonzero divergence for T mu nu (or equivalently the introduction of sources) formally imitates a massive Brans-Dicke and satisfies the condition of Acharya and Hogan that the theory be indistinguishable with the classical test of the Einstein theory. Although it was shown elsewhere that the modified Brans-Dicke theory agrees with the classical test under certain conditions, there were no specified limits on omega, a similar circumstance discovered by Acharya and Hogan for the massive scalar field.