Gravitational lensing in black-bounce spacetimes

In this work, we calculate the deflection angle of light in a spacetime that interpolates between regular black holes and traversable wormholes, depending on the free parameter of the metric. Afterwards, this angular deflection is substituted into the lens equations which allows us to obtain physically measurable results, such as the position of the relativistic images and the magnifications.

Figure 1

The solid (blue) curve describes $I_R(x_m)$ in function of $a/(2M)$. The dashed (red) curve is the value of $I_R(x_m)$ in the Schwarzschild solution, when $a=0$, i.e., $\approx 0.949$.

Figure 2

Angular deflection of light as a function of the impact parameter for various values of the bounce parameter $a$.

Figure 3

Angular deflection of light as a function of $\frac{a}{2M}$, for $\frac{b}{2M}=\frac{3\sqrt{3}}{2}+0.005$.

Figure 4

In this lens diagram, $D_{OL}$ is the distance between the lens $L$ and the observer $O$, and $D_{LS}$ is the distance between the source projection in relation to optical axis and the lens.

Figure 5

Angular separation $s$ as a function of $\frac{a}{2M}$.

Figure 6

$r_m=2,5{\log }_{10}\tilde{r}$ as a function of $\frac{a}{2M}$.