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

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.

arXiv comment10 pages, LaTeX, 1 figure, 1 table (a few typos in the References have been eliminated; the notation for the polynomial in (4.16) is changed)

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