Acoustic black hole evaporation as plasma diffusion phenomena

TL;DR

This paper explores how acoustic black hole analogues in plasmas exhibit evaporation phenomena, linking Hawking temperature to plasma diffusion properties and demonstrating potential laboratory observability.

Contribution

It introduces a model of acoustic black holes in plasmas, connecting Hawking temperature with plasma diffusion and showing evaporation analogies in plasma systems.

Findings

Hawking temperature in plasma torus is approximately 10^{-4} K.

Hawking temperature is proportional to plasma Kelvin temperature.

Plasma black hole evaporation is analogous to diffusive phenomena with inverse mass dependence.

Abstract

Acoustic analogues of Kerr black hole in plasmas are considered, by taking for granted the existence of acoustic ion waves in plasmas. An effective black holes (BH) in curved Riemannian spacetime in a random walk plasmas is endowed with a naked singularity, when plasmas are in the lowest diffusion mode. The plasma particle diffusion is encoded in the effective metric. The diffusive solution has a horizon when the plasma flow reaches the sound velocity in the medium and a shock wave is obtained inside the slab. The sonic black hole curved Riemannian metric is also found in terms of particle number density in plasmas. The sonic BH singularity is found at the center of the plasma diffusive slab from the study of the Ricci curvature scalar for constant diffusion coefficient. It is suggested and shown that the Hawking temperature is proportional to the plasma Kelvin temperature through diffusion coefficient dependence to this temperature. Therefore Unruh sonic or dumb BH is shown to have a relation between Hawking and plasma diffusive temperatures. BH evaporation is analogous to the diffusive phenomena in plasmas, since in both cases Hawking temperature is inversely proportional to mass. It is shown that Hawking analogue temperature of a plasma torus is $T_{H}(torus)\approx{10^{-4}K}$ which is much higher than the gravitational Hawking temperature of a one solar mass BH, ${T_{H}}^{GR}\approx{10^{-8}K}$, but still very small for being detectable in plasma laboratories.