Abstract
Photonspheres, curved hypersurfaces on which massless particles can perform closed geodesic motions around highly compact objects, are an integral part of generic black-hole spacetimes. In the present compact paper we prove, using analytical techniques, that the innermost light rings of spherically symmetric hairy black-hole spacetimes whose external matter fields are characterized by a traceless energy-momentum tensor cannot be located arbitrarily close to the central black hole. In particular, we reveal the physically interesting fact that the non-linearly coupled Einstein-matter field equations set the lower bound \( {r}_{\gamma}\ge \frac{6}{5}{r}_H \) on the radii of traceless black-hole photonspheres, where rH is the radius of the outermost black-hole horizon.
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Acknowledgments
This research is supported by the Carmel Science Foundation. I thank Yael Oren, Arbel M. Ongo, Ayelet B. Lata, and Alona B. Tea for stimulating discussions.
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Hod, S. Lower bound on the radii of light rings in traceless black-hole spacetimes. J. High Energ. Phys. 2023, 178 (2023). https://doi.org/10.1007/JHEP12(2023)178
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DOI: https://doi.org/10.1007/JHEP12(2023)178