### August 25

*and*

**A. Bouchareb, M. Ramon Medrano***have studied*

**N.G. Sanchez***Semiclassical (QFT) and Quantum (String) Rotating Black Holes and their Evaporation*. Quoting freely, the authors compute the quantum emission cross section of strings by a Kerr-Newman black hole. In the early stage of evaporation, the string cross section shows the Hawking part of the emission with temperature Tsem, the semiclassical regime. For Tsem → Ts, the massive string modes dominate the emission, the string cross section shows a Hagedorn phase transition at Tsem = Ts. The last state of evaporation of a semiclassical Kerr-Newman black hole with mass M > mPl, Tsem(J,Q) < Ts, angular momentum J and charge Q is a string state of string temperature Ts, string mass Ms, J = 0 and Q = 0, which decays by the usual quantum string decay into all kinds of particles. Besides the classical/ semiclassical known bounds on J and Q, new bounds emerge in the quantum string regime.

A central object is ρ(m, j), the microscopic string density of states of mass m and spin mode j. They find for the extremal string states j → m^2α′ , a new phase transition at a temperature Tsj = sqrt(j/h)Ts, higher than Ts. They call it

*extremal transition.*The characteristic behavior of this transition is a square root branch point near Tsj . It manifests as a logarithmic singularity in the string entropy S(m, j). This extremal behavior is universal and is analogous to the transition found for the thermal self-gravitating gas of point particles and for strings in de Sitter background.

By identifying the semiclassical and quantum (string) gravity regimes, the authors find a new formula for the Kerr black hole entropy Ssem(M, J), which is a function of the usual Bekenstein-Hawking entropy S(0)sem. For M ≫ mPl^2 and J < GM^2/c, S(0)sem is the leading term of this expression, but for high angular momentum a gravitational phase transition operates and the whole entropy Ssem is drastically different from the Bekenstein-Hawking entropy S(0)sem. This new phase transition takes place at a temperature TsemJ = sqrt(J/h)Tsem, higher than the Hawking temperature Tsem.

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