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

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(infinity)). Additionally, the flux ratio (rmag) 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(infinity)) is found to be within the range of (13.07-26.50) mu as and (10.11-20.51) mu as, respectively, with angular separations (s) ranging from (0.017-0.406) mu as for Sgr A* and (0.013-0.314) mu 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*.