August 25, 2005

August 25

A. Bouchareb, M. Ramon Medrano and N.G. Sanchez have studied 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.