Propagation of massless particles around a BTZ-ModMax black hole

Abstract

We investigate the deflection of light around a BTZ-ModMax black hole, focusing on the influence of the ModMax parameter and the cosmological constant. The trajectories of massless particles are explored through an analysis of null geodesics, providing deeper insights into the gravitational lensing effects in this modified black hole geometry. Using the Gauss-Bonnet theorem, we derive the deflection angle of light and provide a detailed examination of how the ModMax parameter and the cosmological constant impact the bending of light. Furthermore, we compare the deflection results obtained for the BTZ-ModMax black hole with those of the charged and static BTZ black hole solution, highlighting key differences and insights into the role of nonlinear electrodynamics in the gravitational lensing phenomena. This study provides valuable insights into the deflection of light in modified black hole solutions within the framework of lower-dimensional geometry, highlighting the complex relationship between nonlinear dynamics and spacetime curvature.

Figures (9)

• Figure 1: The variation of metric function with radial distance for different values of ModMax and Cosomological constant parameter.
• Figure 2: The variation of effective potential with radial distance for different values of ModMax parameter and and angular momentum of massless particles.
• Figure 3: The graph shows the radii of photon orbit for the ModMax BTZ BH as a function of the ModMax parameter (left panel) and charge parameter (right panel). Here, we consider $m_{0}=1$ and $r_{0}=10$.
• Figure 4: The figure shows three types of photon trajectories around a BH: terminated bound orbit (fall into the singularity), two-world flyby orbit (traverses near the BH and then escape to infinity) and flyby orbit (escape to infinity).
• Figure 5: The graph shows the phase portrait $r$ vs $\dot{r}$ of the null geodesics for different values of the parameter $\gamma$. Here we fix the value of $m_{0}=1$, $q=0.3$, $r_{0}=10$ and $\Lambda=-0.45$.