Non-minimal coupling of torsion–matter satisfying null energy condition for wormhole solutions

Abstract

We explore wormhole solutions in a non-minimal torsion-matter coupled gravity by taking an explicit nonminimal coupling between the matter Lagrangian density and an arbitrary function of the torsion scalar. This coupling describes the transfer of energy and momentum between matter and torsion scalar terms. The violation of the null energy condition occurred through an effective energy-momentum tensor incorporating the torsion-matter non-minimal coupling, while normal matter is responsible for supporting the respective wormhole geometries. We consider the energy density in the form of non-monotonically decreasing function along with two types of models. The first model is analogous to the curvature-matter coupling scenario, that is, the torsion scalar with T -matter coupling, while the second one involves a quadratic torsion term. In both cases, we obtain wormhole solutions satisfying the null energy condition. Also, we find that the increasing value of the coupling constant minimizes or vanishes on the violation of the null energy condition through matter.

Spin, torsion and violation of null energy condition in traversable wormholes

“…This may implicitly suggest that Morris-Thorne wormholes never occur in reality. Interestingly, the above considerations do not apply in general to Einstein Cartan theory [10,11,12,13,14,15,12,16] where non exotic sources of wormholes are possible. In this paper we show how Einstein-Cartan theory allows one to disjoin the flaring out condition from the NEC violation.…”

Revisiting wormhole energy conditions in Riemann-Cartan spacetimes and under Weyl transformations

“…In this case, however, only the first possibility (53) for the transformation of torsion would be meaningful as the other two would not allow for total antisymmetry ofT c ab . Implementing this option inside expression (21), we find the same form for the twist tensor as that of Eq. (22), but decorated of course with tildes.…”

“…[36] twist tensorω ab will keep the same form as in Eq. (21), only decorated everywhere with tildes. Similarly, Raychaudhuri's equation for Riemann-Cartan spacetimes in the form (25), being also a purely geometric equality, implies that the conformally transformed version keeps the same form, only decorated everywhere with tildes.…”

“…In fact, various authors have investigated the issue and came to the following different but complementary conclusions: (i ) torsion might provide the required degree of "exoticity" [20] (ii ) a non-minimal coupling between torsion and matter might relieve the latter from violating the NEC [21] (iii ) for specific values of the matter spin traversable wormholes might definitely be produced without having matter violate the NEC [22]. These possibilities can actually be understood from general backgrounds as follows.…”

“…[5] but seem to agree with those of Refs. [20][21][22], could actually be implemented more rigorously. In so doing, we are going to pinpoint a key fact in Riemann-Cartan spacetimes that has been missed in Ref.…”