Hawking evaporation, shadow images, and thermodynamics of black holes through deflection angle

Abstract We study the Hawking evaporation process of the exact black hole with nonlinear electrodynamics for positive and negative coupling constant ζ. We provide a new perspective to study the thermodynamics of exact black hole through deflection angle formalism. We also evaluate the shadow images in the presence of deflection images for this black hole. Moreover, we consider the Gibbs energy optical dependence to investigate the Hawking-Page transition. We observe that evaporation rate depends upon ζ and black hole evaporates more quickly for positive ζ as compared to negative ζ. For the case =-1 ζ = - 1, the black hole’s lifetime become infinite, which makes the black hole a remnant and the third law of black hole thermodynamics holds in this scenario. We show that the thermal variations in the deflection angle can be used to determine the stable and unstable phases of the black hole. Our findings show that large and small phase transitions of black hole occur at a specific value of the deflection angle.