A Conformal Affine Toda Model of 2D-Black Holes the End-Point State and the S-Matrix

TL;DR

This paper explores a conformal affine Toda model for 2D black holes, revealing a new field redefinition for known solutions and analyzing the quantum scattering matrix, suggesting a non-unitary evolution to a remnant state.

Contribution

It introduces a novel field redefinition within the conformal affine Toda framework and investigates the quantum scattering matrix for black hole states.

Findings

Existence of a range of matter fields leading to a zero temperature remnant

Quantum evolution appears non-unitary, aligning with Hawking's black hole evaporation scenario

Reformulation yields known black hole solutions in the new basis

Abstract

In this paper we investigate in more detail our previous formulation of the dilaton-gravity theory by Bilal--Callan--de~Alwis as a $SL_2$-conformal affine Toda (CAT) theory. Our main results are: i) a field redefinition of the CAT-basis in terms of which it is possible to get the black hole solutions already known in the literature; ii) an investigation the scattering matrix problem for the quantum black hole states. It turns out that there is a range of values of the $N$ free-falling shock matter fields forming the black hole solution, in which the end-point state of the black hole evaporation is a zero temperature regular remnant geometry. It seems that the quantum evolution to this final state is non-unitary, in agreement with Hawking's scenario for the black hole evaporation.