Minimally deformed wormholes

Abstract

Abstract This work is devoted to the study of wormhole solutions in the framework of gravitational decoupling by means of the minimal geometric deformation scheme. As an example, to analyze how this methodology works in this scenario, we have minimally deformed the well-known Morris–Thorne model. The decoupler function f(r) and the $$\theta $$ θ -sector are determined considering the following approaches: (i) the most general linear equation of state relating the $$\theta _{\mu \nu }$$ θ μ ν components is imposed and (ii) the generalized pseudo-isothermal dark matter density profile is mimicked by the temporal component of the $$\theta $$ θ -sector. It is found that the first approach leads to a non-asymptotically flat space-time with an unbounded mass function. To address this issue we have matched both the wormhole and the Schwarzschild vacuum solutions, via a thin-shell at the junction surface. Using the second approach, it can be seen that, on one hand, the solution for $$\gamma =1$$ γ = 1 does not give place to a bounded mass and it presents a topological defect at large distances; on the other hand, the wormhole manifold is asymptotically flat in the $$\gamma =2$$ γ = 2 case. In order to satisfy the flare-out condition, we have found restrictions on the value of the $$\alpha $$ α parameter, which is related with the amount of exotic matter distribution. Finally, the averaged weak energy condition has been analyzed by using the volume integral quantifier.