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This work looks for new wormhole solutions in the non-conservative Rastall gravity. Although Rastall gravity is considered to be a higher-dimensional gravity, the actual diversion from general relativity essentially happens due to a modification in the corresponding matter tensor part. Thus, it would be interesting to find out if such non-minimal coupling has any effect on the traversable wormholes and their corresponding energy conditions.

This work addresses the question whether exotic matter is essential for the formation of wormholes in modified gravity theories. The basic property of wormhole geometry is the flaring-out condition at the throat which essentially states the violation of null energy condition for the matter threading the wormhole in Einstein gravity. In modified gravity theories, the field equations can be written as Einstein equations with two non-interacting fluids of which one is the usual fluid under consideration and the second term, called the effective matter, comes from the extra geometric terms of the theory. So it is interesting to examine whether normal fluid with restrictions on geometry satisfies the conditions for the formation of wormholes and their stability.

The main objective of this paper is to examine the physical features and stability of anisotropic compact stellar objects in energy–momentum squared gravity. For this purpose, we apply Krori–Barua metric solutions and consider three different models of this modified theory to examine the physical characteristics of Her X-1, 4U 1538-52 and SAX J1808.4-3658 compact stars. We analyze the behavior of various physical quantities such as energy density, pressure components, energy conditions, equation of state parameter and anisotropic factor in the interior of these stars. We then use the estimated values of the sound speed and of the adiabatic index to explore the stability of these compact stars. It is found that all the required conditions are satisfied corresponding to all the selected models. We are therefore allowed to conclude that this modified theory provides viable and stable anisotropic compact stars.

The main purpose of this paper is to study the physical characteristics and stability of anisotropic compact stars in energy–momentum squared gravity. We use Tolman $𝕍$ solution and consider specific models of this theory to study the viable features of SAX J1808.4-3658, 4U 1538-52 and Her X-1 stars. We explore the behavior of energy density, pressure components, anisotropic factor, energy conditions and equation of state parameter in the interior of considered stars. To check the stability of these stars, we examine the behavior of causality conditions, Herrera cracking approach and adiabatic index. It is found that all the required conditions are satisfied for the proposed models, thus the considered stars are viable as well as stable in this modified theory.

The main purpose of this paper is to obtain physically stable stellar models coupled with anisotropic matter distribution in the context of $f({ℛ},{\mathrm{\text{T}}}^2)$ theory. For this, we consider a static spherical geometry and formulate modified field equations containing various unknowns such as matter determinants and metric potentials. We then obtain a unique solution to these equations by employing Durgapal–Fuloria ansatz possessing a constant doublet. We also use matching criteria to calculate the values of these constants by considering the Schwarzschild exterior spacetime. Two different viable models of this modified theory are adopted to analyze the behavior of effective matter variables, anisotropy, energy conditions, compactness and redshift in the interiors of Her X-1, PSR J0348-0432, LMC X-4, SMC X-1, Cen X-3, and SAX J 1808.4-3658 star candidates. We also check the stability of these models by using three different physical tests. It is concluded that our considered stars satisfy all the physical requirements and are stable in this modified gravity for the considered parametric values.

In this study, our main purpose is to study a model which is homogenous and anisotropic describing early stage of Universe in non-minimally coupled scalar theory. It is quite interesting to study a model describing early stage in modified theory which is related to scalar field. In this context, we introduced Kantowski–Sachs metric for perfect fluid in non-minimally coupled scalar theory. Exact solution of field equations is attained for $f(R,\varphi )=(1+\xi {\eta }^2{\varphi }^2)R$ model. Matter distributions for radiation, cosmic string and cosmological constant are investigated for constructed model. For different selections of arbitrary constants, Kantowski–Sachs model shows three different behaviors related with Hubble parameter and deceleration parameter. Also, some observational parameters, such as luminosity distance, angular diameter distance and distance modulus, are obtained for Kantowski–Sachs Universe. Lastly, we get Statefinder parameters for the model. All properties of constructed model are discussed from a physical and geometric point of view.

In this paper, some Schwarzschild-like solutions in the framework of $f(T)$ theory where $T$ means the scalar tensor are reconstructed and analyzed in the context of some open problems like traversable wormholes and neutron starts mass limits. Like some authors, we search for the potentiality of the presence of traversable wormholes in the outer/inner regions halo of galaxies particularly the Milky Way galaxy by considering diagonal tetrads which support the Morris–Thorne metric. In such description where attention is attached to the energy density of dark matter present in the halo of spiral galaxies, a new dark matter density emerges in this work. The reconstructed density profile reveals the existence of traversable wormholes not only in the inner of the Milky Way galaxy but also in the both outer and inner of another galaxy smaller than the Milky Way galaxy. The use of Einasto density profile in this work makes it predict traversable wormholes in both outer and inner of the Milky Way galaxy. In the second part of this work, the non-diagonal tetrads describing the Schwarzschild metric are considered to solve the $f(T)$ motion equations, where solutions describing neutron stars are provided. Several numerical analyses based on neutron stars mass are done and the obtained results give the best fit with observational data in the framework of neutron stars mass limit.

In this paper, we investigate in this paper the Type IV singular bouncing in the framework of $f(R,{𝒢})$ theory of gravity where $R$ and ${𝒢}$ mean the curvature scalar and the Gauss–Bonnet invariant, respectively. Cosmological $f(R,{𝒢})$ models constrained by the slow-roll evolution is reconstructed and their explicit forms are provided near the bounce and far away from it. One obtains finally two models whose stability is numerically analyzed in this work. Our results show that the stability of the reconstructed models is very affected by their parameters. The model far from the singularity recovers stability quickly than the model near the singularity.