Photon Sphere for a Dilatonic Dyonic Black Hole in a Model with an Abelian Gauge Field and a Scalar Field

A dilatonic dyonic black hole solution with the gravitational radius $$2\mu$$ and two charges $$Q_{1}$$ and $$Q_{2}$$ (electric and magnetic ones) is considered in a gravitational 4D model with one scalar field and one 2-form, with the dilatonic coupling constant $$\lambda=\pm 1/\sqrt{2}$$ . Circular null geodesics are explored. The 3rd order polynomial master equation for the radius $$R_{0}$$ of photon sphere is studied. There is only one solution with $$R_{0}>2\mu$$ . The circular null geodesics are shown to be unstable. The black hole shadow is studied, and relations for the shadow angle and critical impact parameter are obtained.