Classical and quantal aspects of Minkowski's four-momentum in analog gravity

TL;DR

This paper explores the classical and quantum properties of Minkowski's four-momentum in analog gravity models, focusing on superluminal fluid regions, energy behavior, and particle production, with implications for the Abraham-Minkowski problem.

Contribution

It introduces an artificial model with superluminal regions in analog gravity, analyzing energy, momentum, and particle production, extending previous work on Minkowski's four-momentum.

Findings

Unconventional behavior of radiation energy and momentum in superluminal regions

No particle production detected during horizon creation

Analysis of force on artificial black hole horizon

Abstract

The electrodynamic theory of continuous media is probably the most convenient platform when trying to construct analog gravity theories. Quite naturally, this topic has gained considerable interest. One peculiar but not so very known feature in this context is the unconventional behavior of radiation energy and momentum in cases where superluminal fluid velocities are encountered, what, as known, is a major ingredient in analog gravity theories. These peculiar features are intimately connected with the spacelike character of Minkowski's four-momentum in electrodynamics. Here, we first consider an artificial model in which a Kerr-induced superluminal region is created in the right-hand region ($z>0$) in a left-moving, originally subluminal, fluid. We analyze the behavior of energy density, Poynting vector, and momentum density, and calculate the force on the artificial black hole horizon. Also, we delve into quantal aspects, looking for eventual production of particles associated with the sudden creation of the horizon, finding, however, that no particles are predicted to occur. The present paper continues a previous investigation by the author on the same topic, in Phys. Rev. A {\bf 100}, 032109 (2019). The subject as such is closely related to the famous Abraham-Minkowski problem.