Photon Spheres near Dilatonic Dyon-Like Black Holes in a Model with Two Abelian Gauge Fields and Two Scalar Fields

Dilatonic dyon-like black hole solutions with two (color) charges <span class="mathjax-tex">\(Q_{1}\)</span> and <span class="mathjax-tex">\(Q_{2}\)</span> (electric and magnetic ones) are considered in a gravitational 4D model with two scalar fields and two 2-forms. Two-dimensional dilatonic coupling vectors <span class="mathjax-tex">\(\vec{\lambda}_{i}\)</span>, <span class="mathjax-tex">\(i=1,2\)</span>, determining the model, obey the relation <span class="mathjax-tex">\(\vec{\lambda}_{1}\vec{\lambda}_{2}=1/2\)</span>. Circular null geodesics in the field of such black holes are explored. The master equation for the photon sphere radius <span class="mathjax-tex">\(R\)</span> is derived. A conjecture is suggested on the existence and uniqueness of the solution to the master equation with <span class="mathjax-tex">\(R&gt;R_{g}\)</span>, where <span class="mathjax-tex">\(R_{g}\)</span> is the horizon radius. This conjecture is varified for certain special cases, e.g., for a charge symmetric configuration: <span class="mathjax-tex">\(Q_{1}^{2}=Q_{2}^{2}\)</span>. In this charge symmetric case, we present a relation for the spectrum of quasinormal modes of a test massless scalar field in the eikonal approximation, and an example of circular orbits of a massive particle.