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Photon sphere for a dyonic black hole corresponding to A2 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, Q1 (electric) and Q2 (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 λ2 = 3/2. This solution is related to the A2 Toda chain. The circular orbits of null geodesics are explored, and the fifth-order polynomial master equation governing the photon sphere radius R0 is analyzed. It is shown to admit a unique solution satisfying R0 > 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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Cite

BibTeXRIS
BibTeX
@misc{ivashchuk2026photon,
  title = {{Photon sphere for a dyonic black hole corresponding to $A_2$ Toda chain}},
  author = {Vladimir D. Ivashchuk and Evgeny E. Trubach},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.26421},
  eprint = {2609.26421},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26421},
}
RIS
TY  - UNPB
TI  - Photon sphere for a dyonic black hole corresponding to A_2 Toda chain
AU  - Vladimir D. Ivashchuk
AU  - Evgeny E. Trubach
PY  - 2026
DA  - 2026/09/22
PB  - arXiv
DO  - 10.48550/arxiv.2609.26421
UR  - https://arxiv.org/abs/2609.26421
AB  - 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 = 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.
ER  -