Time evolution of Von Neumann entropy for a Kerr-Taub-NUT black hole

In this work, we study the evolution of an evaporating black hole, described by the Kerr--Taub--NUT metric, which emits scalar particles. We found that allowing the black hole to radiate massless scalar particles increases the angular momentum loss rate while decreasing the loss rate of the NUT parameter and black hole mass. In fact, it means that angular momentum will disappear faster than the other black hole parameters (mass and NUT parameter) during the evaporation process. We also calculate the time evolution of the mass, angular momentum, and NUT parameter in order to get the evolution of the Von Neumann entropy of the black hole. We found that the entropy follows approximately the so-called Page curve, where the $\beta$ parameter, which quantifies the amount of radiation, affects the evaporation process. Implying that high $\beta$ values accelerate the evaporation process of a Kerr--Taub--NUT black hole.