Entanglement entropy of a near-extremal black hole

We study how the entanglement entropy of the Hawking radiation derived using the island recipe for the Reissner–Nordström black hole behaves as the black hole mass decreases. A general answer to the question essentially depends not only on the character of the mass decrease but also on the charge decrease. We assume a specific relation between the charge and mass $Q^2=GM^2[1-(M/\mu)^{2\nu}]$, which we call the constraint equation. We discuss whether it is possible to have a constraint such that the entanglement entropy does not blow up at the end of evaporation, as happens in the case of thermodynamic entropy and the entanglement entropy for the Schwarzschild black hole. We show that for some special scaling parameters, the entanglement entropy of radiation does not blow up if the mass of the evaporating black hole exceeds the Planck mass.