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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]

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]

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]

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]

The primary objective of this study is to conduct a thorough examination of relativistic structures within the framework of f(ℛ,풯 ) gravity, where ℛ is the Ricci scalar and 풯 is the trace of the energy–momentum tensor. We investigate the emerging characteristics of compact stars, focusing on the ℛ + 2ξ풯 model, where ξ is the coupling constant. In the initial sections of the paper, we concentrate on the examination of exact interior solutions involving perfect fluid. With this aim, we introduce the metric coefficient L = S(1 + 2ar2)d/2, where a and S are arbitrary constants to be computed from the matching conditions and d is a positive odd integer. It is worth noticing that we select a group of 10 significant compact stars from recent studies, namely, Vela X − 1, EXO 1785 − 248, 4U1820 − 30, SMCX − 4, HerX − 1, PSR J1614 − 2230, PSRJ1903 + 327, CenX − 3, 4U1538 − 52 and LMCX − 4. To investigate the viability of our model, we conduct various checks, including the analysis of energy density and pressure components, equilibrium, and energy conditions, stability analysis and the adiabatic index. An important part of this work provides the slowly rotating property of stars, accompanied by the derivation of the moment of inertia. The relationship of mass, energy density, radius and moment of inertia for stellar objects are observed. Our findings demonstrate that obtained results are physically acceptable and consistent with our considered model. [ABSTRACT FROM AUTHOR]