Relativistic hydrodynamics under rotation: Prospects and limitations from a holographic perspective

The AdS/CFT correspondence, or holography, has provided numerous important insights into the behavior of strongly-coupled many-body systems. Crucially, it has provided a testing ground for the construction of new effective field theories, especially those in the low frequency, long wavelength limit known as hydrodynamics. We review the study of strongly-coupled rotating fluids using holography, and we examine the hydrodynamics emerging from the study of rotating Myers–Perry black holes. We discuss three regimes in which holographic rotating fluids display either (1) hydrodynamic behavior of a boosted fluid, (2) hydrodynamic behavior distinct from a boosted fluid, or (3) no obvious hydrodynamic behavior. We describe techniques to obtain hydrodynamic and non-hydrodynamic modes, and we compute the radius of convergence for the hydrodynamic regimes. The limitations of hydrodynamics under rotation are discussed alongside our findings.