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

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 nonrotating 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 wave numbers and surface elevation amplitudes of the wave packets are related by simple analytical expressions.

The principle and state-of-art applications of Hawking radiation

“…Figure 5. Schematic diagram of the pseudo-momentum of the pairs of wave packets [13]. Superposition pairs of wave packets with opposite values of pseudo-energy are chosen to ensure that the entangled pairs can be represented by them.…”

Physical Properties of Schwarzschild–deSitter Event Horizon Induced by Stochastic Quantum Gravity

“…These concern, for example, the nature and existence of EHs, their mathematical description, the investigation of quantum and thermodynamics phenomena that can occur in their surroundings, the interaction with particles and fields, and the role of the gravitational field itself [ 12 , 13 , 14 ]. Finally, it is well known that event horizons may be characterized by the occurrence of Hawking radiation [ 15 , 16 , 17 ], as well as energetic particle phenomena and collective interactions [ 18 , 19 , 20 , 21 ]. For this reason, they are also expected to provide the background for quantum field phenomena, like tunneling effects [ 22 , 23 ].…”