Minimally deformed wormholes

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.

Dymnikova-Schwinger traversable wormholes

“…One very common strategy consists in using different state equations in order to obtain those solutions. Some examples can be found in references [21,22]. Among other examples of wormhole solutions with energy density profiles we have the Class one approach [23], the dark matter energy profile [24,25], Yukawa-Casimir wormholes [26], etc.…”

Traversable wormholes with like-Casimir complexity supported with arbitrarily small amount of exotic matter

“…In this regard, given the (theoretical) feasibility of wormholes, the seeking for such geometries is still an active research line (see [3,5] for a self-contained discussion on wormhole. Also see [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25], for recent developments).…”

Construction of a traversable wormhole from a suitable embedding function

“…Since the seminal work by Morris and Thorne [1], the study of traversable wormholes has remain as an attractive research line for many years given the intriguing features it encodes [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. However, the detection of gravitational waves by LIGO/Virgo from the merger of binary black holes [19][20][21] has driven the attention on the possibility of considering wormholes as black holes mimickers [22][23][24].…”