An Intuitive Approach to Analogue Gravity in Bose-Einstein Condensates

Abstract

An analogue gravity model is a physical system in flat spacetime with wave propagation behaving like the propagation of a scalar field of mass m in some curved spacetime. In the first part, we review analogue gravity models with wave propagation governed by a Lagrangian. In this context we propose a novel and more pedagogical approach to constructing massless (m=0) models. While masslessness of the model has often been left without intuitive explanation, we now show that it can be seen as a simple consequence of a certain gauge symmetry present in the analogue system. In the second part, we apply the new approach to re-derive and intuitively explain one of the most important massless models: linear sound in Bose-Einstein condensates in the formalism of second quantization. Specifically, we explain that the masslessness of the model can be traced back to invariance under global phase transformations of the quantized wave function.