The existence of strange matter in compact stars may give rise to striking outcomes of the various physical phenomena. As an alternative to neutron stars, a new class of compact stars called strange stars should exist if the strange matter hypothesis is true. In this paper, we investigate the possible construction of strange stars in quark matter phases based on the MIT bag model. We consider scenarios in which strange stars have no crusts. Then we apply two types of equations of state to quantify the mass–radius diagram for static strange star models, performing the numerical calculation of the modified Tolman–Oppenheimer–Volkoff equations in the context of 4D Einstein–Gauss–Bonnet (EGB) gravity. It is worth noting that the GB term gives rise to a nontrivial contribution to the gravitational dynamics in the limit D → 4. However, the claim that the resulting theory is one of pure gravity has been cast in doubt on several grounds. Thus, we begin our discussion by showing the regularized 4D EGB theory has an equivalent action as the novel 4D EGB in a spherically symmetric spacetime. We also study the effects of coupling constant α on the physical properties of the constructed strange stars including the compactness and criterion of adiabatic stability. Finally, we compare our results to those obtained from standard general relativity.

In this work, the study of traversable wormholes in $f(R)$ massive gravity with the function $f(R)=R+{\alpha }_1{R}^n$, where ${\alpha }_1$ and $n$ are arbitrary constants, is considered. We choose the shape function of the form $b(r)=r\exp (-\alpha (r-r_0))$ with $\alpha$ and $r_0$ being an arbitrary constant and a radius of the wormhole throat, respectively. Here $\alpha$ affects the radius of curvature of the wormhole. We consider a spherically symmetric and static wormhole metric and derive field equations. Moreover, we visualize the wormhole geometry using embedding diagrams. Furthermore, we check the null, weak, dominant, and strong energy conditions at the wormhole throat with a radius $r_0$ invoking three types of redshift functions, $\mathrm{\Phi }=\text{constant}$, ${\gamma }_1/r$, $\log (1+{\gamma }_2/r)$ with ${\gamma }_1$ and ${\gamma }_2$ are arbitrary real constants. We also compute the volume integral quantifier to calculate the amount of the exotic matter near the constructed wormhole throat.