An exact solution for the Hawking effect in a dispersive fluid

TL;DR

This paper provides an exact analytical solution for sound wave propagation in a moving fluid with anomalous dispersion, revealing how dispersion affects Hawking radiation analogs in laboratory systems.

Contribution

It presents an exact solution for dispersive wave scattering in a flowing fluid, extending previous work by Busch and Parentani, and analyzes how dispersion modifies Hawking radiation spectra.

Findings

Exact wave solution in dispersive fluid flow

Dispersion alters the thermal spectrum of Hawking radiation

Classical wave amplification observed in the scattering process

Abstract

We consider the wave equation for sound in a moving fluid with a fourth-order anomalous dispersion relation. The velocity of the fluid is a linear function of position, giving two points in the flow where the fluid velocity matches the group velocity of low-frequency waves. We find the exact solution for wave propagation in the flow. The scattering shows amplification of classical waves, leading to spontaneous emission when the waves are quantized. In the dispersionless limit the system corresponds to a 1+1-dimensional black-hole or white-hole binary and there is a thermal spectrum of Hawking radiation from each horizon. Dispersion changes the scattering coefficients so that the quantum emission is no longer thermal. The scattering coefficients were previously obtained by Busch and Parentani in a study of dispersive fields in de Sitter space [Phys. Rev. D 86, 104033 (2012)]. Our results give further details of the wave propagation in this exactly solvable case, where our focus is on laboratory systems.