Optimization in the Parikh-Wilczek tunneling model of Hawking radiation for Kerr-Newman Black Holes

In this short report, we investigate the mutual information hidden in the Parikh-Wilczek tunneling model of Hawking radiation for Kerr-Newman black holes. By assuming the radiation as an optimization process, we discuss its effect on time evolution of rotating (charged and uncharged) black holes. For uncharged rotating black holes evaporating under the maximum mutual information optimization, their scale invariant rotation parameter $a_*=a/M$ is almost constant at the early stage but rapidly increase at the very last stage of the evaluation process. The value of rotation parameter at the final state of evaporation depends on the initial condition of the black hole. We also found that the presence of electric charge can cause the black holes lose their angular momentum more rapidly than they lose mass. The charged-rotating black holes asymptotically approach a state which is described by $a_*= 0$ and $Q/M = 1$.