Electromagnetic analogue space-times, analytically and algebraically

Abstract

While quantum field theory could more aptly be called the "quantum field framework" $-$ as it encompasses a vast variety of varying concepts and theories $-$ in comparison, relativity, both special and general, is more commonly portrayed as less of a "general framework". Viewed from this perspective, the paradigm of "analogue space-times" is to promote the specific theory of general relativity (Einstein gravity) to a framework which covers relativistic phenomena at large. Ultimately, this then also gives rise to new proposals for experiments in the laboratory, as it allows one to move general features of the "relativistic framework" from general relativity to entirely new fields. This allows experiments looking into analogies of currently unobservable phenomena of general relativity proper. The only requirement for this to work is the presence of a notion of an upper limit for propagation speeds in this new field. Systems of such a kind abound in physics, as all hyperbolic wave equations fulfil this requirement. Consequently, models for analogue space-times can be found aplenty. We shall demonstrate this here in two separate analogue space-time models, both taken from electrodynamics in continuous media. First of all, one can distinguish between analytic analogue models (where the analogy is based on some specific hyperbolic differential equation), on the one hand, and algebraic models (where the analogy is fashioned from the more or less explicit appearance of a metric tensor), on the other hand. Yet this distinction is more than just a matter of taste: The analogue space-time model's nature will also determine which physical concepts from general relativity can be taken easily into an experimental context. Examples of this will the main aim of this paper, and the Hawking effect in one of the two models considered the example of most immediate experimental interest.