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This study explores the new exact solutions of wormhole geometry by imposing the inconsistent Ricci scalar via inhomogeneous spacetime. The current analysis is dealing with the modified f(R, T) theory of gravity. Two different models of gravity that are f1(R) = R − αγtanh(R/γ ) known as exponential gravity model and f1(R) = R − αγ(1-e -R/γ) known as Tsujikawa model, where α, γ are model parameters with matter coupling are considered for the current study. The new feasible solutions for these models by comparing normal and inhomogeneous spacetimes is calculated. Further, we discuss the different properties of the obtained wormhole solutions by taking suitable values of the model parameters analytically and graphically. Moreover, we consider a specific shape functions i.e., b(r) = r0 log( r/r0 + 1) and discuss the energy conditions for both models. The presented wormhole solutions are physically acceptable for the considered exponential and Tsujikawa gravity. [ABSTRACT FROM AUTHOR]

The main emphasis of this paper is to find the viable solutions of Einstein Maxwell field equations of compact star in context of modified f (R) theory of gravity. Two different models of modified f (R) gravity are considered. In particular, we choose isotropic matter distribution and Bardeen's model for compact star to find the boundary conditions as an exterior space-time geometry. We use the conformal Killing geometry to compute the metric potentials. We discuss the behavior of energy density and pressure distribution for both models. Moreover, we analyze different physical properties such as behavior of energy density and pressure, equilibrium conditions, equation of state parameters, causality conditions and adiabatic index. It is noticed that both f (R) gravity models are suitable and provide viable results with Bardeen geometry. [ABSTRACT FROM AUTHOR]

The main idea behind this paper is to study f (, φ) theory of gravity, where is Gauss–Bonnet (GB) term and φ is the scalar field. Scalar field has been introduced to explore gravitational interaction between geometry and scalar field. Field equations in Friedmann–Robertson–Walker (FRW) cosmology are constructed and found to be coherent with the existing literature. Exponential solutions are reconstructed. The coupling of the scalar field to the GB term leads to viable results. Further, we probe the oscillating universe in the said gravity model using linear trace term. Energy conditions are explored and graphically analyzed in detail to substantiate our work. Behavior of the Hubble and deceleration parameter is also examined. It is evident from the results that our model provides us with acceptable bouncing solutions for chosen parameters. [ABSTRACT FROM AUTHOR]

In this paper, we have presented the Einstein–Maxwell equations which are described by the spherically symmetric spacetime in the presence of charge by exploiting the Tolman–Kuchowicz spacetime. The corresponding field equations are constructed and the form of charge distribution is chosen to be Q 0 (r) = Q (r R) 3 = ξ r 3 , where ξ is a constant quantity. We also find the values of unknown constants from junction conditions and discuss the behavior of effective energy density, effective radial and tangential pressure and anisotropic factor with two viable f (R) models. We examine the physical stability of charged stellar structure through energy conditions, causality and stability condition. We use modified form of TOV equation for anisotropic charged fluid sphere to analyze the equilibrium condition. In this work, we model the compact star candidate SAXJ 1808.4 – 3658 and study the compactness level and anisotropic behavior corresponding to the variation of physical parameters which are involved in f (R) models. Further, we evaluate some important properties such as mass-radius ratio compactness factor and surface redshift. It is depicted from this study that the obtained solutions provide strong evidences for more realistic and viable stellar model. [ABSTRACT FROM AUTHOR]

In this paper, we investigate some feasible regions for the existence of wormholes by introducing non-commutative geometry in terms of Gaussian and Lorentzian distributions in f (R , G) modified theory of gravity. We explore wormhole solutions by assuming a viable model f (R , G) = f 1 (R) + f 2 (G) , where f 1 (R) is assumed to be a linear function of Ricci scalar and f 2 (G) is chosen to be a power law model. For f (R , G) model under discussion, we select suitable form of redshift and shape functions, which is necessary for the existence of wormholes. We discuss mainly two types of solutions corresponding to different values of free parameters and obtain numerical results. The stability condition for numerical solutions is discussed via TOV equations and it is proved that gravitational and hydrostatic forces show opposite behavior to anisotropic force and hence cancel each other's effect, which provides a stable wormhole configuration. By using graphical evolution, it has been found that null energy conditions (NEC) are violated for non-commutative Gaussian and Lorentzian distributions. However, some feasible regions have been found for the existence of wormhole solutions with Gaussian and Lorentzian distributions in the context of f (R , G) gravity. [ABSTRACT FROM AUTHOR]

In the current study, we discuss Gödel-type universe in f (R , G) gravity. Analysis has been done by considering anisotropic and perfect fluid distributions. Energy conditions for two proposed f (R , G) gravity models have been studied for suitable values of model parameters. Furthermore, Tolman–Oppenheimer–Volkoff equation has been developed with cylindrical coordinates in f (R , G) gravity. The graphical analysis for both these models suggests that Tolman–Oppenheimer–Volkoff equation is obeyed in a specific interval for the radial coordinate r. A polytropic equation of state has been discussed for two f (R , G) gravity models. By analyzing the energy conditions, it is concluded that Gödel-type universe with both f (R , G) gravity models supports the expansion of the universe for certain range of radial coordinates. [ABSTRACT FROM AUTHOR]

This study reveals the implication of charge within the framework of f(G) gravity models by considering the Tolman–Kuchowicz space–time. The use of the Bardeen model to describe the fundamental characteristics of the external geometry is an important aspect of current findings. Moreover, for the qualitative analysis, we compare all the parameters involved in the selected metric potentials with Bardeen’s model. We apply this analysis to the stars PSR1903 + 327, PSR1937 + 21, PSRJ1614 − 2230, 4U608 − 52, VelaX − 1, LMYX − 4, CenX − 3, HERX − 1, SMXJ1808 − 3658 and 4U1820 − 30. We study all the necessary characteristics of stellar structures, such as energy density and pressure progression, equation of state parameters, equilibrium conditions, mass–radius ratio, adiabatic index, and energy conditions. A thorough graphical analysis is provided to establish the viability of the considered f(G) models. It is important to emphasize that our acquired solutions are physically acceptable. [ABSTRACT FROM AUTHOR]

This study is dedicated to investigate the Noether symmetry approach in a newly introduced gravitational theory known as f(R,G,T) gravity, where f is the function of Ricci scalar R, trace of energy–momentum tensor T, and the Gauss–Bonnet invariant term G. The Noether symmetry approach plays a supportive role in generating models and then determining the exact solutions by using the conserved quantities. For this purpose, the flat Friedmann–Robertson–Walker space–time is selected to observe cosmic evolution. The set of partial differential equations is calculated in the background f(R,G,T) modified theory gravity. We further examine the four different f(R,G,T) gravity models and calculate the conserved quantities to investigate the exact solutions. The three models show the increasing behavior of the cosmic scale factor that supports the expansion of universe. In fourth model, we are able to get the corresponding conserved quantity only and it is anticipated that this model will also support the expansion of universe. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to investigate the exact solutions of cylindrically symmetric spacetime in the context of f( R, T) gravity (Harko et al. in Phys. Rev. D 84:024020, ), where f( R, T) is an arbitrary function of Ricci scalar R and trace of the energy momentum tensor T. We explore the exact solutions for two different classes of f( R, T) models. The first class f( R, T)= R+2 f( T) yields a solution which corresponds to an exterior metric of cosmic string while the second class f( R, T)= f( R)+ f( T) provides an additional solution representing a non-null electromagnetic field. The energy densities and corresponding functions for f( R, T) models are evaluated in each case. [ABSTRACT FROM AUTHOR]

• Exact cylindrically symmetric solutions in the context of Rastall theory of gravity. • The modified field equations in the presence of charge. • To recover the well-known Levi-Civitas static cylindrically symmetric solution in the framework of Rastall gravity. • The graphical behavior of energy density and pressure component along with the discussion of energy conditions. In this paper, we explore some exact cylindrically symmetric solutions in the context of Rastall theory of gravity. For this purpose, we consider the general form of a metric in the cylindrical Weyl coordinates. The modified field equations are developed in the presence of charge. In particular, we try to recover the well-known Levi–Civita's static cylindrically symmetric solution in the framework of Rastall gravity. The graphical behavior of energy density and pressure component is presented along with the discussion of energy conditions. Finally, the solutions in the context of general relativity are discussed. It is concluded that Levi–Civita's static cylindrically symmetric charged solutions do exist in Rastall theory of gravity. [ABSTRACT FROM AUTHOR]

• The study has been performed to analyze the Gödel type universe in modified f (R, ϕ) theory of gravity, where R and ϕ represent the Ricci scalar and scalar potential respectively. • After considering two models of f (R, ϕ) gravity, the corresponding energy conditions are examined through graphs. • The well-known Tolman Oppenheimer Volkoff equation has been studied for both models in this theory. • It is concluded that accelerated expansion of the universe can be justified through Gödel type universe for both models in f (R, ϕ) theory of gravity. The aim of this paper is to study the Gödel type universe in modified f (R, ϕ) theory of gravity, where R stands for Ricci scalar and ϕ be the scalar potential. We investigate the modified field equations by using anisotropic and perfect fluid distributions. In particular, we consider two proposed models with some fixed values of parameters and investigate the exact solutions. The behaviour of energy conditions can be seen by a detailed graphical analysis. Furthermore, Tolman-Oppenheimer-Volkoff equation has been studied for both models in this theory. We have also discussed some exact solutions using perfect fluid. It is concluded that f (R, ϕ) theory of gravity support the phenomenon of cosmic expansion of the universe through Gödel type universe for both models. [ABSTRACT FROM AUTHOR]

The current study examines the geometry of static wormholes with anisotropic matter distribution in the context of modified f () gravity. We consider the well-known Noether and conformal symmetries, which help in investigating wormholes in f () gravity. For this purpose, we develop symmetry generators associated with conserved quantities by taking into consideration the f () gravity model. Moreover, we use the conservation relationship gained from the classical Noether method and conformal Killing symmetries to develop the metric potential. These symmetries provide a strong mathematical background to investigate wormhole solutions by incorporating some suitable initial conditions. The obtained conserved quantity performs a significant role in defining the essential physical characteristics of the shape-function and energy conditions. Further, we also describe the stability of obtained wormholes solutions by employing the equilibrium condition in modified f () gravity. It is observed from graphical representation of obtained wormhole solutions that Noether and conformal Killing symmetries provide the results with physically accepted patterns. [ABSTRACT FROM AUTHOR]

This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the f(τ,T) gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here we consider a linear model within f(τ,T) gravity to investigate traversable wormholes. In particular, we discuss the possible cases for the wormhole geometries using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, we discuss different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, we provide the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks. Moreover, we present the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions. This study explores the Gaussian and the Lorentzian distributed spherically symmetric wormhole solutions in the f(τ,T) gravity. The basic idea of the Gaussian and Lorentzian noncommutative geometries emerges as the physically acceptable and substantial notion in quantum physics. This idea of the noncommutative geometries with both the Gaussian and Lorentzian distributions becomes more striking when wormhole geometries in the modified theories of gravity are discussed. Here the authors consider a linear model within f(τ,T) gravity to investigate traversable wormholes. In particular, the possible cases for the wormhole geometries are considered using the Gaussian and the Lorentzian noncommutative distributions to obtain the exact shape function for them. By incorporating the particular values of the unknown parameters involved, there will be a discussiom of different properties of the new wormhole geometries explored here. It is noted that the involved matter violates the weak energy condition for both the cases of the noncommutative geometries, whereas there is a possibility for a physically viable wormhole solution. By analyzing the equilibrium condition, it is found that the acquired solutions are stable. Furthermore, the embedded diagrams for wormhole structures under Gaussian and Lorentzian noncommutative frameworks are provided. Moreover, the critical analysis on an anisotropic pressure under the Gaussian and the Lorentzian distributions will be presented. [ABSTRACT FROM AUTHOR]