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

TL;DR

This paper analyzes photon spheres and black hole shadows in a dilatonic dyonic black hole model with scalar and gauge fields, revealing unstable null geodesics and specific photon sphere properties.

Contribution

It derives the photon sphere radius and shadow characteristics for a dilatonic dyonic black hole with a specific coupling constant, expanding understanding of null geodesics in such models.

Findings

Photon sphere radius is uniquely determined and exceeds the gravitational radius.

Null geodesics on the photon sphere are unstable.

Explicit relations for shadow angle and impact parameter are obtained.

Abstract

Dilatonic dyon black hole solution with gravitational radius $2 \mu$ and two charges $Q_1$ and $Q_2$ (electric and magnetic ones) in the gravitational $4d$ model with one scalar field and one 2-form is considered. Dilatonic coupling constant $\lambda$ obeys $\lambda^2 = \frac{1}{2}$. The circular orbits for null geodesics are explored. The 3rd order polynomial master equation for radius $R_0$ of photon sphere is studied. It has only one solution which obeys $R_0 > 2 \mu$. The circular null geodesics are shown to be unstable. The black hole shadow is studied and relations for shadow angle and critical impact parameter are obtained.