Complete evaporation of black holes and Page curves

The problem of complete evaporation of Schwarzschild black holes raised by Hawking is that one has an explosion of the temperature $T=1/8πM$ for vanishing black hole mass M. We consider the Reissner-Nordstrom black hole and note that if mass $M$ and charge Q<M satisfy the bound Q>M-C M^3, C>0 for small M then the complete evaporation of black holes without blow-up of temperature is possible. We describe curves on the surface of state equations such that the motion along them provides complete evaporation. The radiation entropy follows the Page curve and vanishes at the end of evaporation. Similar results for rotating Kerr, Schwarzschild-de-Sitter and Reissner-Nordstrom-(Anti)-de-Sitter black holes are discussed.

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