SEMICLASSICAL (QFT) AND QUANTUM (STRING) ROTATING BLACK HOLES AND THEIR EVAPORATION: NEW RESULTS

Combination of both quantum field theory (QFT) and string theory in curved backgrounds in a consistent framework, the string analogue model, allows us to provide a full picture of the Kerr–Newman black hole and its evaporation going beyond the current picture. We compute the quantum emission cross-section of strings by a Kerr–Newman black hole (KNbh). It shows the black hole emission at the Hawking temperature T_sem in the early stage of evaporation and the new string emission featuring a Hagedorn transition into a string state of temperature T_s at the last stages. New bounds on J and Q emerge in the quantum string regime (besides the known ones of the classical/semiclassical QFT regime). The last state of evaporation of a semiclassical Kerr–Newman black hole with mass M > m_Pl, angular momentum J and charge Q is a string state of temperature T_s, string mass M_s, J = 0 and Q = 0, decaying as usual quantum strings do into all kinds of particles. (Naturally, in this framework, there is no loss of information, (there is no paradox at all).) We compute the string entropy S_s(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at T_s) we find for high j (extremal string states j → m²α′c), a new phase transition at a temperature , higher than T_s. By precisely identifying the semiclassical and quantum (string) gravity regimes, we find a new formula for the Kerr black hole entropy S_sem(M, J), as a function of the usual Bekenstein–Hawking entropy . For M ≫ m_Pl and J < GM²/c, is the leading term, but for high angular momentum, (nearly extremal case J = GM²/c), a gravitational phase transition operates and the whole entropy S_sem is drastically different from the Bekenstein–Hawking entropy . This new extremal black hole transition occurs at a temperature T_{sem J} = (J/ℏ)T_sem, higher than the Hawking temperature T_sem.