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arXiv · 2609.26421

Photon sphere for a dyonic black hole corresponding to $A_2$ Toda chain

Vladimir D. Ivashchuk·Evgeny E. Trubach
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Abstract

We consider a dilatonic dyon black hole solution with a gravitational radius of $2 μ$ 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 $λ$ is fixed by $λ^2 = \frac{3}{2}$. 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 $R_0 > 2 μ$. 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.

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Vladimir D. Ivashchuk, Evgeny E. Trubach. 2026-09-22. Photon sphere for a dyonic black hole corresponding to $A_2$ Toda chain. https://doi.org/10.53941/ijgtp.2026.100015

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