Analogue gravity models from conformal rescaling

Abstract

Analogue gravity is based on a mathematical identity between quantum field theory in curved space-time and the propagation of perturbations in certain condensed matter systems. But not every curved space-time can be simulated in such a way. For analogue gravity to work, one needs not only a condensed matter system that generates the desired metric tensor, but this system then also has to obey its own equations of motion. However, the relation to the metric tensor usually overdetermines the equations of the underlying condensed matter system, such that they in general cannot be fulfilled. In this case the desired metric does not have an analogue.Here, we show that the class of metrics that have an analogue is larger than previously thought. The reason is that the analogue metric is only defined up to a choice of parametrization of the perturbation in the underlying condensed matter system. In this way, the class of analogue gravity models can be vastly expanded.