Estimating the cosmological constant from shadows of Kerr--de Sitter black holes

The Event Horizon Telescope collaboration has revealed the first direct image of a black hole, as per the shadow of a Kerr black hole of general relativity. However, other Kerr-like rotating black holes of modified gravity theories cannot be ignored, and they are essential as they offer an arena in which these theories can be tested through astrophysical observation. This motivates us to investigate asymptotically de Sitter rotating black holes wherein interpreting the cosmological constant $\Lambda$ as the vacuum energy leads to a deformation in the vicinity of a black hole -- new Kerr--de Sitter solution, which has a richer geometric structure than the original one. We derive an analytical formula necessary for the shadow of the new Kerr--de Sitter black holes and then visualize the shadow of black holes for various parameters for an observer at given coordinates $(r_0, \theta_0)$ in the domain $(r_0,\; r_c)$ and estimate the cosmological constant $\Lambda$ from its shadow observables. The shadow observables of the new Kerr--de Sitter black holes significantly deviate from the corresponding observables of the Kerr--de Sitter black hole over an appreciable range of the parameter space. Interestingly, we find a finite parameter space for ($\Lambda$, $a$) where the observables of the two black holes are indistinguishable.