Finite width of the sonic event horizon and grey body Hawking radiation

TL;DR

This paper investigates how the finite width of analog event horizons in optical and Bose-Einstein systems affects Hawking radiation, revealing it as a grey body with enhanced emissivity and analyzing the scattering matrix corrections.

Contribution

It introduces a detailed analysis of the finite width effects on Hawking radiation in nonlinear optical and BEC systems, including eigenmode solutions and quantization procedures.

Findings

Hawking radiation appears as a grey body with emissivity > 1

Finite width causes leading order corrections to the scattering matrix

Paraxial quantization links to conventional electromagnetic field quantization

Abstract

Finite width of the analog event horizon is determined by the nonlinearity length in the Kerr nonlinear optical system, which is discussed here, or by the healing length in Bose-Einstein condensates. The various eigen modes of fluctuations are found in the immediate vicinity of the event horizon and the scattering matrix due to the finite width horizon is calculated to within the leading order correction in the nonlinearity length. The Hawking radiation is found to be that of a grey body with the emissivity larger than one. A procedure of paraxial quantization of the fluctuation field is discussed and its connection to the conventional quantization of the electromagnetic field is demonstrated.