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

TL;DR

This paper explores how string theory describes black hole evaporation, revealing a transition from semiclassical Hawking radiation to a string-dominated phase with a minimal black hole size, and introduces a duality linking classical and quantum regimes.

Contribution

It provides a detailed computation of quantum string emission from black holes, identifies a string phase transition, and introduces a duality between classical and string regimes of black holes.

Findings

Black hole temperature transitions from Hawking temperature to string temperature.

Highly massive string states dominate emission near the string phase transition.

Existence of a minimal black hole with a finite lifetime and a duality mapping between regimes.

Abstract

String theory properly describes black-hole evaporation. The quantum string emission by Black Holes is computed. The black-hole temperature is the Hawking temperature in the semiclassical quantum field theory (QFT) regime and becomes the intrinsic string temperature, T_s, in the quantum (last stage) string regime. The QFT-Hawking temperature T_H is upper bounded by the string temperature T_S. The black hole emission spectrum is an incomplete gamma function of (T_H - T_S). For T_H << T_S, it yields the QFT-Hawking emission. For T_H \to 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 string back reaction effect (selfconsistent black hole solution of the semiclassical Einstein equations) is computed. Both, the QFT and string black hole regimes are well defined and bounded.The string `minimal' black hole has a life time tau_{min} simeq (k_B c)/(G hbar [T_S]^3). 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 regimes.