Image of Kerr-de Sitter black holes illuminated by equatorial thin accretion disks

To explore the influence of the cosmological constant on black hole images, we have developed a comprehensive analytical method for simulating images of Kerr-de Sitter black holes illuminated by equatorial thin accretion disks. Through the application of explicit equations, we simulate images of Kerr-de Sitter black holes illuminated by both prograde and retrograde accretion disks, examining the impact of the cosmological constant on their characteristic curves, relative sizes, and observed intensities. Our findings reveal that, in comparison to Kerr black holes, the cosmological constant not only diminishes the relative size of a black hole but also amplifies its luminosity. Moreover, an observer's relative position in the universe ($r_0/r_C$) can influence both the relative size and luminosity of a black hole, where $r_0$ is the distance from the observer to the black hole, $r_C$ is the cosmological horizon determined by the value of the cosmological constant $\Lambda$.