Microlensing effect of a charged spherically symmetric wormhole

We systematically investigate the microlensing effect of a charged spherically symmetric wormhole, where the light source is remote from the throat. Remarkably, there will be at most three images by considering the charge part. We study all the situations including three images, two images, and one image, respectively. The numerical result shows that the range of total magnification is from ${10}^5$ to ${10}^{-2}$ depending on various metrics. In the case of three images, there will be two maximal values of magnification (a peak and a gentle peak) when the contribution via mass is much less than that of charge. However, we cannot distinguish the case that forms three images or only one image as the total magnification is of order ${10}^5$. Finally, our theoretical investigation could shed new light on exploring the wormhole with the microlensing effect.

Figure 1

The lensing geometry via the wormhole source depicted by the blue ball $W$, in which the corresponding potential is (14). $O$ denotes the observer and $S$ is the source of light. The image is represented by $I$. $\alpha$ is the deflection angle and $\beta$ is the angle between the wormhole and light source. $\tilde{\beta }$ is the angle between the image and light source. $b$ is the impact parameter that is perpendicular to dotted line $OS$. $D_{ls}$, $D_l$, and $D_s$ are the angular diameter distances. For simplicity, we set $D_{ls}\approx D_l$. $z$ varies from $S$ to $O$.

Figure 2

The contour plot of ${\mu }_{\text{total}}$ in terms of ${\theta }_{\mathrm{E},\mathrm{Q}}$ and $b$ as fixing ${\theta }_{\mathrm{E},\mathrm{M}}={10}^{-7}$. We have set $0<b<0.2\mathrm{kpc}$, $D_l=10\mathrm{kpc}$, $0<{\theta }_{\mathrm{E},\mathrm{Q}}<1$.

Figure 3

The plot of ${\mu }_{\text{total}}$ in terms of ${\theta }_{\mathrm{E},\mathrm{Q}}$ and $b$ as fixing ${\theta }_{\mathrm{E},\mathrm{M}}={10}^{-7}$. We have set $0<b<10\mathrm{kpc}$, $D_l=10\mathrm{kpc}$, ${\theta }_{\mathrm{E},\mathrm{M}}={10}^{-7}$, ${\theta }_{\mathrm{E},\mathrm{Q}}=0.1$, ${\theta }_{\mathrm{E},\mathrm{Q}}=0.2$, ${\theta }_{\mathrm{E},\mathrm{Q}}=0.3$ and ${\theta }_{\mathrm{E},\mathrm{Q}}=.4$.

Figure 4

The plot of ${\mu }_{\text{total}}$ in terms of ${\theta }_{\mathrm{E},\mathrm{M}}$ and $b$. In the upper panel, we fix ${\theta }_{\mathrm{E},\mathrm{Q}}={10}^{-4}$ and ${\theta }_{\mathrm{E},\mathrm{M}}=0.8$. The lower panel shows ${\ln }_{10}({\mu }_{\text{total}})$ in terms of ${\theta }_{\mathrm{E},\mathrm{Q}}$ and $b$ as fixing ${\theta }_{\mathrm{E},\mathrm{Q}}={10}^{-4}$. We have set $0<b<0.03\mathrm{kpc}$, $D_l=10\mathrm{kpc}$.

Figure 5

The upper panel is the contour plot of ${\mu }_{\text{total}}$ in terms of ${\theta }_{E,M}$ and $b$ as fixing ${\theta }_{\mathrm{E},\mathrm{Q}}=0.45$. We have set $0<b<1\mathrm{kpc}$, $D_l=10\mathrm{kpc}$. In the lower panel is the contour plot of ${\ln }_{10}({\mu }_{\text{total}})$ in terms of ${\theta }_{\mathrm{E},\mathrm{Q}}$ and $b$ as fixing ${\theta }_{\mathrm{E},\mathrm{M}}=0.45$. We have set $0<b<1\mathrm{kpc}$, $D_l=10\mathrm{kpc}$.

Figure 6

The contour plot of ${\mu }_{\text{total}}$ in terms of ${\theta }_{\mathrm{E},\mathrm{Q}}$ and $b$ as fixing ${\theta }_{\mathrm{E},\mathrm{Q}}=0.1$. We have set $0<b<1\mathrm{kpc}$, $D_l=10\mathrm{kpc}$.

Figure 7

We have set $0<b<{10}^{-3}\mathrm{kpc}$, $0<x<\frac{1}{3}$ and $D_l=10\mathrm{kpc}$ with $x={\theta }_{\mathrm{E},\mathrm{M}}^2$.

Figure 8

The upper panel shows that contour plot of ${\ln }_{10}({\mu }_{\text{total}})$, in which we have set ${\theta }_{\mathrm{E},\mathrm{M}}={10}^{-4}$ and $0<b<0.1\mathrm{kpc}$, $0<{\theta }_{\mathrm{E},\mathrm{Q}}<0.1$. The lower panel shows the contour plot of ${\mu }_{\text{total}}$ with ${\theta }_{\mathrm{E},\mathrm{Q}}={10}^{-4}$ and $0<b<0.1\mathrm{kpc}$, $0<{\theta }_{\mathrm{E},\mathrm{M}}<1$.

Figure 9

The upper panel shows the contour plot of ${\mu }_{\text{total}}$. We have set ${\theta }_{\mathrm{E},\mathrm{M}}=0.8$ and $0<b<0.1\mathrm{kpc}$, $0<{\theta }_{\mathrm{E},\mathrm{Q}}<0.1$. In the lower panel, contour plot of ${\mu }_{\text{total}}$ with ${\theta }_{\mathrm{E},\mathrm{Q}}=0.8$ and $0<b<0.1\mathrm{kpc}$, $0<{\theta }_{\mathrm{E},\mathrm{M}}<0.11$.