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

Abstract

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 Ts 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 Ts, string mass Ms, 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 Ss(m, j) from the microscopic string density of states of mass m and spin mode j, ρ(m, j). (Besides the Hagedorn transition at Ts) we find for high j (extremal string states j → m2α′c), a new phase transition at a temperature [Formula: see text], higher than Ts. 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 [Formula: see text]. For M ≫ m Pl and J < GM2/c, [Formula: see text] 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 [Formula: see text]. This new extremal black hole transition occurs at a temperature T sem J = (J/ℏ)T sem , higher than the Hawking temperature T sem .