Conical Morris-Thorne Wormholes with a Global Monopole Charge.

In this paper we have established an asymptotically conical Morris-Thorne wormhole solution with a global monopole charge in the framework of a $1+3$ dimensional gravity minimally coupled to a triplet of scalar fields $\phi^a$, resulting from the breaking of a global $O(3)$ symmetry. We have considered the equation of state (EoS) given by $\mathcal{P}_r=\omega \rho$, with a consequence $\omega<-1$, implying a so-called phantom energy at the throat of the wormhole which violates the energy conditions. The peculiar conical topology of the spacetime makes it suitable to study the gravitational lensing effect. In doing so, we have used the Gauss-Bonnet theorem (GBT) which leads to an exact result for the total deflection angle in leading-order terms. The total angle consists by a purely topological term which is independent of the impact parameter $4\pi^2 \eta^2 $, and a purely geometric term which depends on the radius of the wormhole throat and the parameter $\omega$. To this end, we also address the problem of the stability of a thin-shell around a conical traversable wormhole (TSCTW), in which we find stable domains for suitable values of parameters. Furthermore we find that energy conditions such as NEC and WEC are satisfied.