Strong gravitational lensing by black hole in F(R) Euler Heisenberg Gravity's Rainbow

Abstract

We investigate gravitational lensing in the strong-field regime for a black hole in F(R) Euler Heisenberg Gravity with Rainbow gravity modifications. This black hole spacetime is characterized by the Euler Heisenberg parameter, F(R) parameters, Rainbow functions, the black hole charge Q, and mass M . We numerically compute the strong deflection angle and its associated coefficients, and explore their astrophysical implications for supermassive black holes in different galaxies. Our findings show that increasing the Euler Heisenberg parameter enhances key lensing observables such as the photon sphere radius, critical impact parameter, angular position, relative magnification, Einstein ring radius, and time delay for a fixed Q . Conversely, increasing Q decreases these parameters while keeping other quantities fixed. Additionally, a higher Euler Heisenberg parameter reduces the deflection angle and angular separation S , whereas increasing Q causes both to increase. Our study reveals that black holes in this modified gravity framework can act as strong gravitational lenses, producing deflection angles that surpass those of Reissner Nordstrom and Schwarzschild black holes under specific conditions. These results highlight the unique topological features of modified charged black holes and suggest their potential as astrophysical candidates, offering new insights into their observational signatures. Furthermore, we analyze the sensitivity of the lensing predictions with respect to changes in the functional forms of the Rainbow functions. The combined effects of F(R) gravity, Euler Heisenberg electrodynamics, and Rainbow gravity introduce novel qualitative features not present in the individual models.