Vorticity in analogue spacetimes

TL;DR

This paper investigates the challenges and possibilities of modeling rotating astrophysical spacetimes with angular momentum using analogue models, focusing on the role of vorticity in the medium's flow.

Contribution

It explores the extent to which analogue models can incorporate vorticity to simulate astrophysical spacetimes with angular momentum.

Findings

Acoustic analogue models work best without vorticity.

Modeling rotating spacetimes requires incorporating vorticity.

The paper discusses potential methods to include vorticity in analogue models.

Abstract

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 $[g_\mathrm{eff}(g,V,\,\Xi)]_{ab}$. These effective metrics generically depend on some physical background metric $g_{ab}$, often flat Minkowski space $\eta_{ab}$, some "medium" with 4-velocity $V^a$, and possibly some additional background fields $\Xi$. 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).