Entanglement entropy of near-extremal black hole

Abstract

We study how the entanglement entropy of the Hawking radiation derived using island recipe for the Reissner-Nordstr\"om black hole behaves as the black hole mass decreases. A general answer to the question essentially depends not only on the character of decreasing of the mass but also on decreasing of the charge. We assume the specific relationship between the charge and mass $Q^2=GM^2[1-\left(\frac{M}{\mu}\right)^{2\nu} ]$, which we call the constraint equation. We discuss whether it is possible to have a constraint so that the entanglement entropy does not have an explosion 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 explode as long as the mass of the evaporating black hole exceeds the Planck mass.