PreprintarXiv licencearXiv
An end-to-end function for the photograph of a Schwarzschild black hole
Abstract
We show that the photograph of a Schwarzschild black hole can be written in closed form. The image plane is embedded as a plane tangent to a sphere centred on the black hole, and the map between a point source and its image point, which we call the photograph function, is treated as the analytic object. Explicit expressions are obtained for sources on the celestial sphere at infinity and for sources in the equatorial plane, without solving for the intermediate null geodesics. The construction is exact, and it makes the multivalued branch structure, the relation to the photon sphere and to the shadow boundary, and the self-similar higher-order images directly readable.
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BibTeX
@misc{li2026endtoend,
title = {{An end-to-end function for the photograph of a Schwarzschild black hole}},
author = {Ping Li and Jun Cheng and Jiang-he Yang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29437},
eprint = {2610.29437},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29437},
}
RIS
TY - UNPB
TI - An end-to-end function for the photograph of a Schwarzschild black hole
AU - Ping Li
AU - Jun Cheng
AU - Jiang-he Yang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29437
UR - https://arxiv.org/abs/2610.29437
AB - We show that the photograph of a Schwarzschild black hole can be written in closed form. The image plane is embedded as a plane tangent to a sphere centred on the black hole, and the map between a point source and its image point, which we call the photograph function, is treated as the analytic object. Explicit expressions are obtained for sources on the celestial sphere at infinity and for sources in the equatorial plane, without solving for the intermediate null geodesics. The construction is exact, and it makes the multivalued branch structure, the relation to the photon sphere and to the shadow boundary, and the self-similar higher-order images directly readable.
ER -