Testing strong gravitational lensing effects of supermassive black holes with string-inspired metric: Observational signatures and EHT constraints

Abstract

We analyze gravitational lensing in the strong field limit for spherically symmetric string-inspired Euler–Heisenberg black holes, characterized by magnetic charge ($q$) and Einstein–Maxwell-dilaton coupling constants ($\alpha ,\beta$) from the low-energy limit of heterotic string theory. Our results show that the string coupling has a weak impact on the positions of relativistic images, deflection angles, photon orbit radii, and shadow sizes, making these black holes indistinguishable from the Gibbons–Maeda–Garfinkle–Horowitz–Strominger (GMGHS) black holes with the same mass and charge. Compared to Schwarzschild black holes, the string-inspired Euler–Heisenberg black holes exhibit smaller deflection angles, decreasing with increasing charge. Moreover, the time delay for Sgr A * and M87 * can reach $11.477$ and $17349.8$ min, respectively, at $q=0.1$ and $\eta =-1$, deviating from Schwarzschild black holes by $0.0198$ and $28.9$ min, which are not very significant. For Sgr A* and M87*, we determine ${\theta }_{\infty }$ range within $(11.52,26.33)\mu$as, and $(9.17,19.78)\mu$as respectively, with angular separations $s$ ranging from $(3.29\text{–}6.85)$ nas for Sgr A* and $(2.47\text{–}5.15)$nas for M87*. EHT bounds on the ${\theta }_{sh}$ of Sgr A* and M87* within the $1\sigma$ interval bound the $q$ as: for Sgr A* $0.54109\le q\le 0.7796$ and for M87* $0<q\le 0.29107$, while in both the cases, we did not find any bound on the parameter $\eta$. We show that string-inspired Euler–Heisenberg black holes and EHT observations agree in the finite parameter space. A discussion on the effective metric has been included.