Analogue gravity: between analogy and emergence

Analogue gravity focuses on the analogy between the fields that propagate through gravitational fields and the perturbations that propagate in continuous media that can be tested experimentally, media with well-studied and well-known behaviors. In this relation between the specific gravitational case and all the others, emphasis is placed on the first because it is the one which is particularly difficult to examine directly with experiments, while the systems with which the analogy is established are those in which experiments and measures can be made. In this work we investigate the nature of the analogy between systems made with Bose--Einstein condensates and gravitational systems, with the aim of studying how the analogy can be extended, what deductions can be drawn and what perspectives open towards a broader understanding of gravity. In particular, analogue models in which gravitational phenomena can be simulated consist of (classical or quantum) perturbations propagating in a medium, an analogue spacetime. The description of the medium is made in terms of the classical and continuum limit of a microscopic underlying structure, and it is therefore emergent from a more fundamental theory.