Conical Morris-Thorne Wormholes with a Global Monopole Charge

Abstract

In this paper we have established an asymptotically conical Morris-Thorne wormhole solution supported by anisotropic matter fluid and a global monopole charge in the framework of a $1+3$ dimensional gravity minimally coupled to a triplet of scalar fields ${\varphi }^a$, resulting from the breaking of a global $O(3)$ symmetry. For the anisotropic matter fluid 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. In addition, we study the weak gravitational lensing effect using the Gauss-Bonnet theorem (GBT) applied to the wormhole optical geometry. We show that the total deflection angle consists of a term given by $4{\pi }^2{\eta }^2$, which is independent from the impact parameter $b$, and an additional term which depends on the radius of the wormhole throat $b_0$ as well as the dimensionless constant $\zeta$.

8 pages, 4 figures, accepted for publication in Physical Review D

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