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Wormholes (WHs) are hypothetical topologically non‐trivial spacetime structures that can be freely traversed by observers and connect two asymptotic regions or infinities. From the current theoretical development, the prospect of their existence is challenging but cannot be excluded. In this paper, generalized Ellis–Bronikov (GEB) traversable WH geometries for static and spherically symmetric spacetime in the background of f(R)$f(R)$ gravity is explored. First, the Tsujikawa‐like f(R)$f(R)$ model and the shape function for the GEB model is considered, which depend on a sequence of simple Lorentzian WHs with two parameters: a free even integer exponent, n, besides the throat radius, r0. One also consider that these WHs are generated by dark matter galactic halos (DMGHs), based on the three most common phenomenological models, viz., Navarro–Frenk–White (NFW), Thomas–Fermi (TF), and pseudo‐isothermal (PI). In this concern, the satisfaction of the energy conditions (ECs) which are dependent on the dark matter (DM) models, viz., dominant energy condition (DEC) and strong energy condition (SEC) and those which are not dependent viz., null energy condition (NEC) and WEC at the WH throat and its neighborhood is investigated. Finally, the presence of exotic matter is confirmed by the violation of the NEC in all cases, revealing the supremacy and physical acceptability to support the existence of the WHs and making them compatible and traversable in Tsujikawa's‐like f(R)$f(R)$ model. [ABSTRACT FROM AUTHOR]

In this article, we provide a new model of static charged anisotropic fluid sphere made of a charged perfect fluid in the context of 5D Einstein–Maxwell–Gauss–Bonnet (EMGB) gravity theory. To generate exact solutions of the EMGB field equations, we utilize the well-behaved Tolman–Kuchowicz (TK) ansatz together with a linear equation of state (EoS) of the form p r = β ρ - γ , (where β and γ are constants). Here the exterior space-time is described by the EGB Schwarzschild metric. The Gauss–Bonnet Lagrangian term L GB is coupled with the Einstein–Hilbert action through the coupling constant α . When α → 0 , we obtain the general relativity (GR) results. Here we present the solution for the compact star candidate EXO 1785-248 with mass = (1.3 ± 0.2) M ⊙ ; radius = 10 - 1 + 1 km. respectively. We analyze the effect of this coupling constant α on the principal characteristics of our model, such as energy density, pressure components, anisotropy factor, sound speed etc. We compare these results with corresponding GR results. Moreover, we studied the hydrostatic equilibrium of the stellar system by using a modified Tolman–Oppenheimer–Volkoff (TOV) equation and the dynamical stability through the critical value of the radial adiabatic index.The mass-radius relationship is also established to determine the compactness factor and surface redshift of our model. In this way, the stellar model obtained here is found to satisfy the elementary physical requirements necessary for a physically viable stellar object. [ABSTRACT FROM AUTHOR]

In their seminal work, Morris and Thorne (1988) introduced the concept of traversable wormholes (WHs), which are geometric structures serving as bridges to connect two distinct spacetimes or different points within the same spacetime. The properties of these WHs are determined by the choice of the shape function. Extensive research has been conducted in the literature on WHs within modified theories of gravity, considering various types of shape functions. In this paper, we focus on deriving the simplest solutions for traversable WHs within the framework of f (R , T) gravity. Our specific focus lies on the functional form f (R , T) = R + α R 2 + λ T , where R represents the Ricci scalar and T denotes the trace of the energy–momentum tensor. By incorporating quadratic geometric and linear material corrections, we demonstrate that the matter content of WHs can obediently conform to the energy conditions (ECs). This study significantly advances our understanding of WHs within the context of modified gravity. Our findings shed new light on the behavior and properties of WHs, highlighting their compatibility with the f (R , T) gravity framework. By unveiling the ability of WHs to adhere to ECs through the inclusion of geometric and material corrections, we provide groundbreaking insights into these intriguing objects. Overall, our research contributes to the broader field of gravitational physics by presenting a unique perspective on WH modeling. By exploring WHs within the f (R , T) gravity framework and demonstrating their conformity to ECs, we expand our knowledge of these fascinating structures and pave the way for further investigations in this area. [ABSTRACT FROM AUTHOR]

This study is devoted to explore the physical aspects of wormhole geometry under embedded class-1 spacetime in f (T , τ) gravity, where τ denotes the trace of the energy-momentum tensor and T is the torsion. We derive the embedded class-1 solutions by considering spherically symmetric static spacetime. The shape function is calculated in the framework of embedded class-1 spacetime. It is necessary to mention here that the calculated shape function can be used in other modified theories of gravity. To complete this study, we take diagonal and off-diagonal tetrad, and try to build a comparison by considering the validity region of energy conditions in embedded class-1 spacetime. The embedded surface diagram is given to understand the connection between the two different regions of spacetime. The validity regions of all the energy conditions are calculated. A detailed graphical analysis is provided for validity regions of all the energy conditions. The presence of exotic matter is confirmed in both the cases as the null energy condition is violated. [ABSTRACT FROM AUTHOR]

The main focus of this paper is to explore the possibility of providing a new family of exact solutions for suitable anisotropic spherically symmetric systems in the realm of general relativity involving the embedding spherically symmetric static metric into the five-dimensional pseudo-Euclidean space. In this regard, we ansatz a new metric potential λ (r) , and we obtained the other metric potential ν (r) by mains of embedding class one approach. The unknown constants are determined by the matching of interior space-time with the Schwarzschild exterior space-time. The physical acceptability of the generating celestial model for anisotropic compact stars is approved via acting several physical tests of the main salient features viz., energy density, radial and tangential pressures, anisotropy effect, dynamical equilibrium, energy conditions, and dynamical stability, which are well-compared with experimental statistics of four different compact stars: PSR J1416-2230, PSR J1903+327, 4U 1820-30 and Cen X-3. Conclusively, all the compact stars under observations are realistic, stable, and are free from any physical or geometrical singularities. We find that the embedding class one solution for anisotropic compact stars is viable and stable, plus, it provides circumstantial evidence in favor of super-massive pulsars. [ABSTRACT FROM AUTHOR]