Analogue spacetimes can be used to probe and study physically interesting spacetime geometries by constructing, either theoretically or experimentally, some notion of an effective Lorentzian metric [g eff (g, V, Ξ)] ab . These effective metrics generically depend on some physical background metric g ab , often flat Minkowski space η ab , some "medium" with 4-velocity V a , and possibly some additional background fields Ξ. Electromagnetic analogue models date back to the 1920s, acoustic analogue models to the 1980s, and BEC-based analogues to the 1990s. The acoustic analogue models have perhaps the most rigorous mathematical formulation, and these acoustic analogue models really work best in the absence of vorticity, if the medium has an irrotational flow. This makes it difficult to model rotating astrophysical spacetimes, spacetimes with non-zero angular momentum, and in the current article we explore the extent to which one might hope to be able to model astrophysical spacetimes with angular momentum, (thereby implying vorticity in the 4-velocity of the medium). (Stefano Liberati), sebastian.schuster@sms.vuw.ac.nz (Sebastian Schuster ), gtricell@sissa.it (Giovanni Tricella), matt.visser@sms.vuw.ac.nz (Matt Visser ) the exercises in the Landau-Lifshitz volume on classical field theory [6]. Scientific interest in these electromagnetic analogues is ongoing, see for instance [7,8,9,10,11,12,13,14,15], and references therein.In 1981 Unruh developed the acoustic analogue spacetimes (subsequently called dumb holes) [16], with further developments due to one of the present authors [17,18,19]. While these early acoustic models were based on ordinary barotropic fluid mechanics, much subsequent work was based on the "Madelung fluid" interpretation of a quantum condensate wave-function -typically a non-relativistic or relativistic BEC [20,21,22,23,24,25, 26,27,28]. Such analogue models have been applied in mimicking several interesting spacetimes. However, angular momentum in the physical spacetime to be mimicked corresponds to vorticity in the flow of the arXiv:1802.04785v2 [gr-qc]

Analogue gravity can be used to reproduce the phenomenology of quantum field theory in curved spacetime and in particular phenomena such as cosmological particle creation and Hawking radiation. In black hole physics, taking into account the backreaction of such effects on the metric requires an extension to semiclassical gravity and leads to an apparent inconsistency in the theory: the black hole evaporation induces a breakdown of the unitary quantum evolution leading to the so called information loss problem. Here we show that analogue gravity can provide an interesting perspective on the resolution of this problem, albeit the backreaction in analogue systems is not described by semiclassical Einstein equations. In particular, by looking at the simpler problem of cosmological particle creation, we show, in the context of Bose-Einstein condensates analogue gravity, that the emerging analogue geometry and quasi-particles have correlations due to the quantum nature of the atomic degrees of freedom underlying the emergent spacetime. The quantum evolution is, of course, always unitary, but on the whole Hilbert space, which cannot be exactly factorised a posteriori in geometry and quasi-particle components. In analogy, in a black hole evaporation one should expect a continuous process creating correlations between the Hawking quanta and the microscopic quantum degrees of freedom of spacetime, implying so that only a full quantum gravity treatment would be able to resolve the information loss problem by proving the unitary evolution on the full Hilbert space.