Remarks on the black hole shadows in Kerr-de Sitter space times

TL;DR

This paper analyzes the shadows of Kerr-de Sitter black holes, comparing them with Kerr black holes, and uses observational data to constrain black hole parameters, finding that certain shadows are indistinguishable under specific cosmological constant values.

Contribution

It provides a detailed analysis of black hole shadows in Kerr-de Sitter spacetimes and compares them with Kerr black holes, incorporating observational constraints from M87* data.

Findings

Kerr-de Sitter and Kerr black hole shadows are indistinguishable at certain cosmological constants.

Observers near the static radius can derive impact parameters for shadow positions.

Constraints on black hole parameters are obtained from M87* observations.

Abstract

This work is geared towards analysis of shadows cast by Kerr-de Sitter (KdS) and Kerr-de Sitter Revisited (RKdS) black holes. Considering observers in the vicinity of the static radius, we derive the impact parameters defining the apparent positions of the shadows. Such observers are of interest to our work because embedding diagrams have shown that de Sitter space-time is analogous to an asymptotically flat one in the vicinity of the static radius. We also perform a comparative analysis between our result with that in Ref.[1]. Furthermore, we numerically obtain the radii of curvature, vertical diameters and horizontal diameters of the shadows. We find that for $\Lambda=1.11\times 10^{-52} m^{-2}$, M87* observations cannot distinguish a RKdS black hole shadow from that of a Kerr black hole. Additionally, for the same value of $\Lambda$, KdS and RKdS black hole shadows are identical. Previously, it has also been shown that when $\Lambda=1.11\times 10^{-52} m^{-2}$, KdS and Kerr black hole shadows are indistinguishable. Utilizing the 2017 EHT observations of M87* on the allowed range of the characteristic radius of the shadow, we obtain constraints on both black holes. When, a/M>0.812311, we observe that large angles of inclination ($\theta>30.5107^{\circ}$) do not pass the constraints for both KdS and RKdS black holes.