Universal quantum Hawking evaporation of integrable two-dimensional solitons

TL;DR

This paper demonstrates that two-dimensional integrable solitons can undergo Hawking-like evaporation, linking soliton dynamics with black hole physics through a universal geometric and quantum anomaly framework.

Contribution

It introduces a universal method to associate a spacetime metric with 2D integrable solitons, enabling the calculation of Hawking radiation properties for these solutions.

Findings

Solitons emit Hawking radiation analogous to black holes.

The method applies to solitons of nonlinear Schrödinger, KdV, and sine-Gordon equations.

The approach connects integrable systems with quantum black hole phenomena.

Abstract

We show that any soliton solution of an arbitrary two-dimensional integrable equation has the potential to eventually evaporate and emit the exact analogue of Hawking radiation from black holes. From the AKNS matrix formulation of integrability, we show that it is possible to associate a real spacetime metric tensor which defines a curved surface, perceived by the classical and quantum fluctuations propagating on the soliton. By defining proper scalar invariants of the associated Riemannian geometry, and introducing the conformal anomaly, we are able to determine the Hawking temperatures and entropies of the fundamental solitons of the nonlinear Schroedinger, KdV and sine-Gordon equations. The mechanism advanced here is simple, completely universal and can be applied to all integrable equations in two dimensions, and is easily applicable to a large class of black holes of any dimensionality, opening up totally new windows on the quantum mechanics of solitons and their deep connections with black hole physics.