Hawking Radiation in String Theory and the String Phase of Black Holes

The quantum string emission by Black Holes is computed in the framework of the “string analogue model” (or thermodynamical approach), which is well suited to combine QFT and string theory in curved backgrounds (particulary here, as black holes and strings posses intrinsic thermal features and temperatures). The QFT-Hawking temperature TH is upper bounded by the string temperature TS in the black hole background. The black hole emission spectrum is an incomplete gamma function of (TH − TS). For TH TS , it yields the QFT-Hawking emission. For TH → TS , it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic “minimal” black hole of mass Mmin or radius rmin (inversely proportional to TS) and string temperature TS . The semiclassical QFT black hole (of mass M and temperature TH) and the string black hole (of mass Mmin and temperature TS) are mapped one into another by a “Dual” transform which links classical/QFT and quantum string regimes. The string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations with mass M+ (radius r+) and temperature T+) is computed. Both, the QFT and string black hole regimes are well defined and bounded: rmin ≤ r+ ≤ rS , Mmin ≤ M+ ≤ M , TH ≤ T+ ≤ TS. The string “minimal” black hole has a life time τmin ' kBc Gh̄ T−3 S .