AI 中文总结
该论文研究了一个与 $A_2$ Toda 链相关的 dyonic 黑洞，分析了其光子球半径满足的五次方程，证明了唯一解的存在性和圆轨道的非稳定性，并给出了黑洞阴影角与临界碰撞参数的关系。
AI 中文摘要
我们在一个包含一个标量场和一个 2-形式的四维引力模型框架内，考虑了一个具有引力半径 $2 \mu$ 和两个电荷 $Q_1$（电）与 $Q_2$（磁）的膨胀 dyonic 黑洞解。膨胀耦合常数 $\lambda$ 由 $\lambda^2 = \frac{3}{2}$ 固定。该解与 $A_2$ Toda 链相关。我们探索了零测地线的圆轨道，并分析了控制光子球半径 $R_0$ 的五次多项式主方程。该方程被证明存在唯一满足 $R_0 > 2 \mu$ 的解。圆零测地线被证明是不稳定的。最后，我们研究了黑洞阴影，得到了阴影角和临界碰撞参数的关系。
英文摘要
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.
Comments15 pages, 2 figures, 1 table, LaTex
Journal refInternational Journal of Gravitation and Theoretical Physics, 2 (3), 1 (2026)
DOI：10.53941/ijgtp.2026.100015
