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In this work, we employ the class I approach to obtain wormhole solutions in the framework of general relativity in two different ways. Firstly, we propose a suitable red-shift function in order to find its associated shape function. Afterwards, we solve the inverse problem, namely, we impose the well known Morris–Thorne shape function to obtain the corresponding red-shift. It is found that, on one hand, the first model satisfies all the general requirements of a traversable wormhole. On the other hand, although the second solution violates the null energy condition at the throat as expected, the solution is not asymptotically flat. The study is complemented by analyzing the hydrostatic balance of the system by means of the modified relativistic hydrostatic equilibrium equation. • Analytical wormhole solutions by embedding class I in general relativity. • Morris–Thorne wormhole space–time with a non null red-shift function. • The solutions fulfill the geometrical requirements to represent traversable wormholes. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain analytic relativistic anisotropic spherical solutions in f (R , T) scenario. To do so we use modified Durgapal–Fuloria metric potential and the pressure anisotropy condition is imposed in order to obtain the effective anisotropic factor Δ ̃. Besides, a notable and viable election on f (R , T) gravity formulation is taken. The choice of f (R , T) function modifies the matter sector only, including new ingredients to the physical parameters that characterize the model such as density, pressure, subliminal speeds of sound, surface redshift etc. We analyze all the physical and mathematical general requirements of the configuration taking M = 1. 04 M ⊙ and varying χ from − 0. 1 to 0.1. It is shown by the graphical procedure that χ < 0 yields a more compact object in comparison when χ ≥ 0 (where χ = 0. 0 corresponds to general relativity) and increases the value of the surface redshift. However, negative values of χ introduce in the system an attractive anisotropic force (inward) and the configuration is completely unstable (corroborated employing Abreu's criterion). Furthermore, the model in Einstein gravity theory presents cracking while for χ > 0 the system is fully stable. The relationship between effective radial pressure p ̃ r and effective density ρ ̃ is discussed and obtained. This is achieved by establishing the corresponding equation of state. • We have obtained new analytic relativistic anisotropic spherical solutions for modified Durgapal–Fuloria potential in the framework of f (R , T) gravity theory. • We use pressure anisotropy condition to obtain a physically viable expression for effective anisotropic factor (Δ). • We have shown that the present f (R , T) model is stable while the cracking appears inside the model in case of Einstein's gravity (GR) which shows that the f (R , T) gravity theory could be more useful to discover the stable model than the Einstein theory. • We established the relationship between pressure and density as p = f (ρ) and discovered an approximate equation of state for the present model. [ABSTRACT FROM AUTHOR]