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In this work, we generate curved Lorentzian manifolds from a flat Minkowskian space–time, through the Gravitational Decoupling by the Minimal Geometric Deformation method interpreting the decoupling sector as a generator of curvature and matter distribution. In particular, we obtain some new wormhole geometries by imposing either physically relevant equations of state or certain physically–motivated geometric constraints. These solutions are analyzed in detail. For all these solutions, we study the associated energy conditions, the geometric behavior and construct their embedding diagrams. [ABSTRACT FROM AUTHOR]

We present a simple and effective new methodology to build up self-gravitating structures driven by an imperfect fluid distributions. This approach is developed within the framework of f (R , T) gravity theory by combining two geometrical schemes, the gravitational decoupling by means of minimal geometric deformation and the embedding technique, specifically the class I grasp. The former, allows to introduce extra matter fields into the system, modifying the energy–momentum tensor, as well as new degrees of freedom altering the mass function and its associated metric potential, i.e, the g r r component. On the other hand the class I focusing, provides precious and useful mathematical information to determine the full geometrical description of the internal spacetime. Furthermore, to obtain the final form of the modified material content the so-called mimic constraint procedure is employed. To check the mathematical, physical and astrophysical viability of the present proposal, we have framed a detailed discussion on the matching condition process and studied the effects introduced by the mimic constraint approach on the mass function. Finally, to support the feasibility of the results a thorough graphical analysis is performed. [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]