Аңдатпа
This paper investigates the optical characteristics of a static spherically symmetric dilatonic black hole. The primary objective of the study is to examine the effect of the dilatonic charge Q and the dilaton coupling parameter a on the shadow geometry and the structure of Einstein rings. The research methodology is based on numerical simulations using the backward ray-tracing method, employing the Lagrangian formalism for the photon equations of motion. The main results show that an increase in the dilatonic parameters leads to a significant "compactification" effect of the shadow, the diameter of which can decrease by 31% relative to the Schwarzschild limit at extreme parameter values. Furthermore, a characteristic visual thickening of higher-order photon rings is observed, while maintaining complete topological stability of the image. The scientific value of this work lies in identifying specific optical signatures that allow distinguishing dilatonic black holes from the classical objects of General Relativity. The practical significance of the results is related to their potential application in interpreting observational data from the Event Horizon Telescope (EHT) and searching for manifestations of physics beyond standard models. Keywords: Dilatonic Black holes, Ray tracing, Lensing images, Shadow geometry.