Pairs of surface wave packets with zero-sum energy in the Hawking radiation analog

TL;DR

This paper proposes a minimal analog gravity setup using surface wave packets with zero-sum energy to mimic Hawking radiation, demonstrating key features of black hole horizon physics through controlled wave interactions.

Contribution

It introduces a novel wave packet configuration with equal wave action but opposite energies to simulate virtual particle creation near black hole horizons.

Findings

Wave packets with opposite energies can mimic Hawking radiation.

Analytical expressions relate wave packet properties like wavenumber and amplitude.

The model satisfies Hawking's low frequency mode amplification prediction.

Abstract

Here we propose a minimal analog gravity setup and suggest how to select two surface gravity wave packets in order to mimic some key aspects of Hawking radiation from the horizon of non-rotating black holes. Our proposed setup, unlike the scattering problem conventionally studied, constitutes of a constant mean flow over a flat bathymetry, in which the two wave packets possess the same amount of wave action but equal and opposite (sign) amount of energy, thereby mimicking virtual particles created out of near horizon vacuum fluctuations. Attention is given to the physical mechanism relating to the signs of the wave action and energy norm with the wave's intrinsic and total phase speeds. We construct narrow wave packets of equal wave action, the one with positive energy and group speed propagates against the mean flow and escapes from the black hole as Hawking radiation, while the other with negative energy and group speed is drifted by the mean flow and falls into it. Hawking's prediction of low frequency mode amplification is satisfied in our minimal model by construction. We find that the centroid wavenumbers and surface elevation amplitudes of the wave packets are related by simple analytical expressions.