Topologically Charged Morris-Thorne-type Wormholes and the Energy Conditions

In this paper, we investigate topologically charged Morris-Thorne-type traversable wormholes by solving the Einstein field equations with an anisotropic fluid as the energy-momentum tensor and analysing the resulting solutions. In continuation to the earlier work (Eur. Phys. J C {\bf 84} (2024) 1037), we consider the shape functions such as: (i) $A(r)=r_0\,e^{r_0-r}$; (ii) $A(r)=r_0\,a^r/a^{r_0}$,\quad $0 < a<1$; (iii) $A(r)=r_0\,\left(\frac{\cosh r_0}{\cosh r}\right)^{\delta}$,\quad $\delta \geq 1$; (iv) $A(r)=\frac{1}{r}+\ln\!\frac{r}{r_0}$; (v) $A(r)=B\,r^n+(1-B)$; (vi) $A(r)=r_0\,\frac{\mbox{ln} (1+r)}{\mbox{ln} (1+r_0)}$, (vii) $A(r)=r_0+a\,r_0\,\left[\left(\frac{r}{r_0}\right)^\beta-1\right]$, where $\beta<1$ and $0 < a\,\beta <1$. We examine the energy conditions-namely, null, weak, strong, and dominant energy conditions and explore how topological charge influences or controls these conditions. Additionally, we calculate the anisotropy parameter to determine whether the wormhole geometry exhibits attractive or repulsive behavior. Our analysis demonstrates that the energy density of the anisotropic fluid is always positive. However, while some of the energy conditions are partially satisfied, others are violated.