Testing low energy string theory with strong gravitational lensing by black holes and constraints from EHT observations

Abstract

We explore strong-gravitational lensing by spherically symmetric Dyon black holes, characterized by the parameters $\lambda$ and $\beta$, which are releated to the electric and magnetic charges within low-energy string theory. Our study reveals that as the values of $\lambda$ and $\beta$ increase, there is a decrease in the photon sphere radius ($x_m$), the critical impact parameter ($u_m$), and the angular position (${\theta }_{\infty }$). Additionally, the flux ratio ($r_{mag}$) of the first image to all other images decreases with increasing $\lambda$ and $\beta$. In contrast to Schwarzschild black holes (where $\lambda$ and $\beta$ approach 0), these Dyon black holes show a smaller deflection angle (${\alpha }_D$), which further decreases as $\lambda$ and $\beta$ increase. Furthermore, the time delay for black holes such as Sgr A* and M87* can reach up to approximately 10.011 and 15133.1 min, respectively, deviating from Schwarzschild black holes by about 1.4858 and 2245.8 min. For Sgr A* and M87*, the angular position (${\theta }_{\infty }$) is found to be within the range of (13.07–26.50) $\mu \mathrm{as}$ and (10.11–20.51) $\mu \mathrm{as}$, respectively, with angular separations ($s$) ranging from (0.017–0.406) $\mu \mathrm{as}$ for Sgr A* and (0.013–0.314) $\mu \mathrm{as}$ for M87*. The Event Horizon Telescope (EHT) constraints on ${\theta }_{sh}$ for Sgr A* and M87* within the 1$\sigma$ region limit the parameters $\lambda$ and $\beta$ such that the allowed values of $\beta$ depend on the parameter $\lambda$. For Sgr A* $0.184M^2<\beta <0.508M^2$ and $0<\beta <0.138M^2$ for M87* when $\lambda =0.4M$. Our results imply that Dyon black holes, inspired by low-energy string theory, match EHT observations within a specific parameter space, indicating that these black holes could be convincing candidates for astrophysical black holes. We also estimate the parameters $\lambda$ and $\beta$ for string-inspired Dyon black holes using EHT observation results for Sgr A* and M87*.