https://doi.org/10.1140/epjc/s10052-025-15183-w
Regular Article - Theoretical Physics
Optical appearance of Schwarzschild black holes with optically thin and thick accretion disks at various inclination angles
School of Physics, Guizhou University, 550025, Guiyang, China
Received:
10
October
2025
Accepted:
6
December
2025
Published online:
6
January
2026
In this paper, we systematically investigate the optical appearance of a Schwarzschild black hole illuminated by three geometrically thin accretion disk models under varying observational inclination angles. Based on the geometric relationship between the black hole and observer, we first divide the accretion disk into co-side and counter-side semi-disks. We then analyze light ray trajectories, and calculate the total number of orbits and transfer functions for both semi-disks. The results reveal distinct inclination-dependence of lensed regions on different semi-disks: as inclination increases, the lensed region contracts for the counter-side semi-disk while expanding for the co-side one. Furthermore, through explicit specification of the emission profiles of the three models, we present optical images for both optically thin and thick disk scenarios at different inclinations. The results demonstrate that: (i) the bright rings in all three models become progressively compressed and deviate from circularity as inclination increases; (ii) for thick disks, partial rings are obscured and the overall intensity is lower than thin disks. These results may advance our understanding of general black hole imaging processes and provide a new approach to test gravitational theories through optical morphology studies.
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
