The String Phases of Hawking Radiation, De Sitter Stage and De Broglie Type Duality

TL;DR

This paper explores the final stages of black hole evaporation using string theory, revealing a duality between semiclassical and quantum gravity regimes and describing a phase transition to string states at the end of evaporation.

Contribution

It explicitly describes the last stages of black hole evaporation within string theory, establishing a duality between semiclassical and quantum gravity regimes and detailing the phase transition to string states.

Findings

Black hole evaporation spectrum involves an incomplete gamma function of temperature difference.

At the end of evaporation, black holes transition to string states decaying into pure particles.

Semiclassical and quantum gravity regimes are shown to be dual to each other.

Abstract

We explicitly describe the last stages of black hole evaporation in the context of string theory : the combined study of Quantum Field Theory (QFT) and String Theory (ST) in curved backgrounds allows us to go further in the understanding of quantum gravity effects. The string ``analogue model''(or thermo-dynamical approach) is a well suited framework for this purpose.The results also apply to another physically relevant case: de Sitter background. Semiclassical (QFT) and quantum gravity (String) phases or regimes are properly determined (back reaction effects included). The Hawking-Gibbons temperature ${T_H}$ of the semiclassical regime becomes the intrinsic string temperature ${T_S}$ in the quantum gravity regime.The spectrum of black hole evaporation is an incomplete gamma function of $(T_S - T_H)$: the early evaporation is thermal (Hawking radiation), while at the end the black hole undergoes a phase transition to a string state decaying (as string decay) into pure (non mixed) particle states.Remarquably, explicit dynamical computations show that both gravity regimes: semiclassical (QFT) and quantum (string), are dual of each other, in the precise sense of the classical-quantum (de Broglie type) duality.