Optical properties and thermal geometries of hot NUT–Kerr–Newman–Kasuya AdS spacetime

This paper is devoted to studying the optical and thermal geometrical properties of Hot NUT–Kerr–Newman–Kasuya-anti-de Sitter (HNKNK-AdS) black hole. This black hole is characterized by the NUT charge and a parameter Q that comprises the electric [Formula: see text] and magnetic mono-pole parameter [Formula: see text] (Kasuya parameter). We compute the image of the BH shadow in two types: (1) at [Formula: see text], (2) at [Formula: see text] by analytical approach. We also investigate the effect of NUT, spin, inclination angle, and cosmological constant on the shape of shadow. We analyze that for type 1, the shadow in increasing for higher values of NUT charge, the cosmological constant, rotation parameters, and inclination angle, while for type 2, by increasing these parameters, the circular symmetry of the image of the BH shadow variate. Moreover, we discuss well-known thermal geometries such as Weinhold, Ruppeiner, HPEM and Quevedo case I and II spacetime. It is found that Ruppeiner, HPEM and Quevedo (II) formulations provide physical information about the microscopic structure as compared to Weinhold and Quevedo (I) geometries. Our findings provide distinctive characteristics in the shadow and thermal geometries of this BH as compared to other black holes types.