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

Abstract

Dilatonic dyon-like black hole solutions with two (color) charges \(Q_{1}\) and \(Q_{2}\) (electric and magnetic ones) are considered in a gravitational 4D model with two scalar fields and two 2-forms. Two-dimensional dilatonic coupling vectors \(\vec{\lambda}_{i}\), \(i=1,2\), determining the model, obey the relation \(\vec{\lambda}_{1}\vec{\lambda}_{2}=1/2\). Circular null geodesics in the field of such black holes are explored. The master equation for the photon sphere radius \(R\) is derived. A conjecture is suggested on the existence and uniqueness of the solution to the master equation with \(R>R_{g}\), where \(R_{g}\) is the horizon radius. This conjecture is varified for certain special cases, e.g., for a charge symmetric configuration: \(Q_{1}^{2}=Q_{2}^{2}\). 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.