Thermodynamical and optical behavior of a loop quantum gravity black holes in de Sitter spacetime

Understanding the properties of the light ring in rotating black holes (BHs) and the equatorial timelike circular orbits in non-rotating BHs is made possible by the study of topology. This work aims to identify the zero points corresponding to various orbital configurations of circular orbits within the temporal dimension that are distinguished by the distinct topology in loop quantum gravity (LQG) BH in de Sitter (dS) spacetime. We created a vector in the r - \(\theta\) plane using the effective potential, and the zero points of \(\phi\) which represent the locations of the timelike circular orbits. We determine the topology connected to the timelike circular orbits because of this special characteristic. Simple, connected horizons are represented by zeros of winding number, whereas more complex topologies, like multi-sheeted horizons, are represented by winding numbers that are nonzero. Moreover, we also find the shadow, optical appearance, and interpretation of intensity under the influence of different parameters involving in LQGBH in dS spacetime and compare theoretical depiction of BH shadow diameter with real images of M87* and SgrA*.