We consider a dilatonic dyon black hole solution with a gravitational radius of \(2\mu\) and two charges, \(Q_1\) (electric) and \(Q_2\) (magnetic), within the framework of a four-dimensional gravitational model comprising one scalar field and one 2-form. The dilaton coupling constant \(\lambda\) is fixed by \(\lambda^2 = \frac{3}{2}\). This solution is related to the \(A_2\) Toda chain. The circular orbits of null geodesics are explored, and the fifth-order polynomial master equation governing the photon sphere radius \(R_0\) is analyzed. It is shown to admit a unique solution satisfying \(R_0 > 2\mu\). The circular null geodesics are proven to be unstable. Finally, the black hole shadow is examined, yielding relations for the shadow angle and the critical impact parameter.
- Open Access
- Article
Photon Sphere for a Dyonic Black Hole Corresponding to A2 Toda Chain
- Vladimir D. Ivashchuk 1,2,*,
- Evgeny E. Trubach 3
Author Information
Received: 26 Jul 2026 | Revised: 10 Sep 2026 | Accepted: 11 Sep 2026 | Published: 17 Sep 2026
Abstract
Keywords
black hole | photon sphere | dyon | Toda chain | black hole shadow
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