Black Hole Emission in String Theory and the String Phase of Black Holes

Abstract

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 quantum field theory (QFT) and string theory in curved backgrounds (particulary here, as black holes and strings posses intrinsic thermal features and temperatures).String theory properly describes black-hole evaporation. The black-hole temperature is the Hawking temperature in the semiclassical (QFT) regime and becomes the intrinsic string temperature, Ts, in the quantum (last stage) string regime.The QFT-Hawking temperature T H is upper bounded by the string temperature T s in the black hole background. The black hole emission spectrum is an incomplete gamma function of (T H-Ts). For T H ≪ T S , it yields the QFT-Hawking emission. For T H → T s, it shows highly massive string states dominate the emission and undergo a typical string phase transition to a microscopic ‘minimal’ black hole of mass M min or radius r min (inversely proportional to T S) and string temperature T S .The semiclassical QFT black hole (of mass M and temperature T H) and the string black hole (of mass M min and temperature T S ) are mapped one into another by a ‘Dual’ transform which links classical/QFT and quantum string regimesThe 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: r min ≤r +≤r S M min ≤ M + ≤ M, T H ≤ T+ ≤T S .The string “minimal” black hole has a life time τmin \( \simeq \frac{{k_B c}} {{G\hbar }}T_S^{ - 3} \).KeywordsBlack HoleOpen StringBlack Hole Space TimeCanonical Partition FunctionBlack Hole EvaporationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.